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Locally convex topological vector space
mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X
Reflexive_space
mathematics known as functional analysis, a semi-reflexive space is a locally convex topological vector space (TVS) X such that the canonical evaluation map
Semi-reflexive_space
mathematics, a polynomially reflexive space is a Banach space X, on which the space of all polynomials in each degree is a reflexive space. Given a multilinear
Polynomially_reflexive_space
Topics referred to by the same term
up reflexive in Wiktionary, the free dictionary. Reflexive, or the property reflexivity, may refer to: Metafiction Reflexivity (grammar): Reflexive pronoun
Reflexive
Normed vector space that is complete
X j {\displaystyle X_{j}} is reflexive. Hilbert spaces are reflexive. The L p {\displaystyle L^{p}} spaces are reflexive when 1 < p < ∞ . {\displaystyle
Banach_space
A be a linear operator defined on a linear subspace D(A) of the reflexive Banach space X. Then A generates a contraction semigroup if and only if A is
Lumer–Phillips_theorem
isometrically isomorphic to its double dual, while not being reflexive. Furthermore, James' space has a basis, while having no unconditional basis. Let P {\displaystyle
James'_space
space – Type of topological vector space Reflexive space – Locally convex topological vector space Semi-reflexive space Schaefer & Wolff 1999, p. 142. Jarchow
Infrabarrelled_space
normed space X is uniformly smooth if and only if ρX(t ) / t tends to 0 as t tends to 0. Every uniformly smooth Banach space is reflexive. A Banach space X
Uniformly_smooth_space
Scalar-valued bilinear function
reflexivity we have to distinguish left and right orthogonality. In a reflexive space the left and right radicals agree and are termed the kernel or the
Bilinear_form
Indirect control over an opponent's decisions
Reflexive control is control someone has over their opponent's decisions by imposing on them assumptions that change the way they act. Methods of reflexive
Reflexive_control
Vector space of infinite sequences
As a consequence ℓ q {\displaystyle \textstyle \ell ^{q}} is a reflexive space. By abuse of notation, it is typical to identify ℓ q {\displaystyle
Sequence_space
Topics referred to by the same term
Quasi-reflexive may refer to: Quasi-reflexive relation Quasi-reflexive space This disambiguation page lists articles associated with the title Quasi-reflexive
Quasi-reflexive
Generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
false if one replaces the space C c ∞ {\displaystyle C_{c}^{\infty }} with L 2 {\displaystyle L^{2}} (which is a reflexive space that is even isomorphic
Nuclear_space
operator in A. This should not be confused with a reflexive space. Nest algebras are examples of reflexive operator algebras. In finite dimensions, these
Reflexive_operator_algebra
Tsirelson space is the first example of a Banach space in which neither an ℓ p space nor a c0 space can be embedded. The Tsirelson space is reflexive. It was
Tsirelson_space
way to deal with the fact that the Sobolev space W1,1 is not a reflexive space; since W1,1 is not reflexive, it is not always true that a bounded sequence
Souček_space
General concept and operation in mathematics
theorem. As a corollary, every Hilbert space is a reflexive Banach space. The dual normed space of an Lp-space is Lq where 1/p + 1/q = 1 provided that
Duality_(mathematics)
TVS whose strong dual is barralled
bornological space. All normed spaces and semi-reflexive spaces are distinguished spaces. LF spaces are distinguished spaces. The strong dual space X b ′ {\displaystyle
Distinguished_space
Topological vector space in which every closed and bounded subset is complete
of quasi-complete spaces is again quasi-complete. Every semi-reflexive space is quasi-complete. The quotient of a quasi-complete space by a closed vector
Quasi-complete_space
Continuous dual space endowed with the topology of uniform convergence on bounded sets
bounded subsets Reflexive space – Locally convex topological vector space Semi-reflexive space Strong topology Topologies on spaces of linear maps Schaefer
Strong_dual_space
Type of vector space in math
that a Hilbert space H is reflexive, meaning that the natural map from H into its double dual space is an isomorphism. In a Hilbert space H, a sequence
Hilbert_space
Concept in mathematics of vector spaces
In mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity was
Uniformly_convex_space
Concept in linear algebra
V^{**}} (which is not identical to V {\displaystyle V} ). However, the reflexive spaces have a natural isomorphism i {\displaystyle i} between V {\displaystyle
Orthogonal_complement
Banach space Hahn–Banach theorem Dual space Predual Weak topology Reflexive space Polynomially reflexive space Baire category theorem Open mapping theorem
List of functional analysis topics
List_of_functional_analysis_topics
Vector space in mathematics
linear operator between two Banach spaces is weakly compact if and only if it factors through a reflexive space. The space ℓ q used for the discrete definition
Interpolation_space
Branch of mathematics that studies dynamical systems
strongly continuous one-parameter semigroup of contractive operators on a reflexive space. Remark: Some intuition for the mean ergodic theorem can be developed
Ergodic_theory
isometrically isomorphic to its double dual, but fails to be reflexive. Tsirelson space, a reflexive Banach space in which neither ℓ p {\displaystyle \ell ^{p}} nor
List_of_Banach_spaces
2021 film by Malcolm D. Lee
Space Jam: A New Legacy is a 2021 American live-action animated sports comedy film, directed by Malcolm D. Lee. A sequel to Space Jam (1996), the film
Space_Jam:_A_New_Legacy
Reflexive and transitive binary relation
in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders are
Preorder
Mathematics concept
spaces and reflexive spaces All metrizable spaces. In particular, all Fréchet spaces, including all Banach spaces and specifically Hilbert spaces, are Mackey
Mackey_space
Mathematical set with an ordering
comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short)
Partially_ordered_set
Function spaces generalizing finite-dimensional p norm spaces
For 1 < p < ∞ , {\displaystyle 1<p<\infty ,} the space L p ( μ ) {\displaystyle L^{p}(\mu )} is reflexive. Let κ p {\displaystyle \kappa _{p}} be as above
Lp_space
Mathematics lemma in functional analysis
{\displaystyle y} in Y . {\displaystyle Y.} If X {\displaystyle X} is a reflexive Banach space then this conclusion is also true when α = 1. {\displaystyle \alpha
Riesz's_lemma
Order whose elements are all comparable
{\displaystyle c} in X {\displaystyle X} : a ≤ a {\displaystyle a\leq a} (reflexive). If a ≤ b {\displaystyle a\leq b} and b ≤ c {\displaystyle b\leq c} then
Total_order
In mathematics, vector space of linear forms
the corresponding notion of reflexivity is the standard one: the spaces reflexive in this sense are just called reflexive. If V ′ {\displaystyle V'} is
Dual_space
Type of topological vector space
boundedly summing TVS. A locally convex Hausdorff reflexive space is barrelled. A barrelled space need not be Montel, complete, metrizable, unordered
Barrelled_space
Reflexivity of uniformly convex Banach spaces
the Milman–Pettis theorem states that every uniformly convex Banach space is reflexive. The theorem was proved independently by D. Milman (1938) and B. J
Milman–Pettis_theorem
mathematics, the reflexive closure of a binary relation R {\displaystyle R} on a set X {\displaystyle X} is the smallest reflexive relation on X {\displaystyle
Reflexive_closure
Vector space with a partial order
vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with the vector space operations
Ordered_vector_space
Subspace preserved by a linear mapping
singular (or compact) operator acting on a real infinite-dimensional reflexive space. Invariant manifold Lomonosov's invariant subspace theorem Roman 2008
Invariant_subspace
In algebraic geometry, a reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The
Reflexive_sheaf
Theorem on extension of bounded linear functionals
I . {\displaystyle i\in I.} If X {\displaystyle X} happens to be a reflexive space then to solve the vector problem, it suffices to solve the following
Hahn–Banach_theorem
Topological vector spaces
three spaces, are complete nuclear Montel bornological spaces, which implies that all six of these locally convex spaces are also paracompact reflexive barrelled
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
1998 video game
published for Microsoft Windows by Reflexive Entertainment. The action is viewed from a top-down perspective in outer space and uses pre-rendered 3D graphics
Swarm_(1998_video_game)
Operation on the subsets of a set
operations of it. For examples: Reflexivity As every intersection of reflexive relations is reflexive, we define the reflexive closure of R {\displaystyle
Closure_(mathematics)
Partially ordered vector space, ordered as a lattice
Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are
Riesz_space
Topics referred to by the same term
result that a Banach space is reflexive if and only if its closed unit ball is compact in the weak topology: see Reflexive space#Properties. the Birkhoff-Kakutani
Kakutani's_theorem
Binary relation over a set and itself
with (for affine spaces) Equinumerosity or "is in bijection with" Isomorphic Equipollent line segments Tolerance relation, a reflexive and symmetric relation:
Homogeneous_relation
Duality for locally compact abelian groups
reflective groups. In 1952 Marianne F. Smith noticed that Banach spaces and reflexive spaces, being considered as topological groups (with the additive group
Pontryagin_duality
of the double dual V ″ . {\displaystyle V''.} The space V {\displaystyle V} is a semi-reflexive space if and only if this map is surjective. The f : X
Pettis_integral
Algebraic element satisfying some of the criteria of an inverse
{\displaystyle A} . If it satisfies the first two conditions, then it is a reflexive generalized inverse of A {\displaystyle A} . If it satisfies all four
Generalized_inverse
Function space of all functions whose derivatives are rapidly decreasing
dual space are also: complete Hausdorff locally convex spaces, nuclear Montel spaces, ultrabornological spaces, reflexive barrelled Mackey spaces. If
Schwartz_space
lemma Riesz's lemma. reflexive A reflexive space is a topological vector space such that the natural map from the vector space to the second (topological)
Glossary of functional analysis
Glossary_of_functional_analysis
Type of topology in mathematics
preorder on the space. Spaces with an Alexandrov topology are also known as Alexandrov-discrete spaces or finitely generated spaces. The latter name
Alexandrov_topology
Well-quasi-ordering of finite trees
Chain-complete Eulerian Graded Locally finite Strict Prefix order Preorder Total Reflexive Semilattice Semiorder Symmetric Tolerance Total Transitive Well-founded
Kruskal's_tree_theorem
Mathematical concept for comparing objects
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments
Equivalence_relation
Certain topology in mathematics
(possibly infinitely many) such open intervals and rays. A topological space X is called orderable or linearly orderable if there exists a total order
Order_topology
Open-air or naturally-lit large space surrounded by a building
atrium (pl.: atria or atriums) is a large open-air or skylight-covered space surrounded by a building. Atria were a common feature in Ancient Roman dwellings
Atrium_(architecture)
Space of bounded sequences
{\displaystyle \ell ^{\infty }} is not a reflexive Banach space. L ∞ {\displaystyle L^{\infty }} is a function space. Its elements are the essentially bounded
L-infinity
Chmeee) is a junior diplomat, trained to deal with other species without reflexively killing them. He is recruited by Nessus, a Pierson's Puppeteer, as a
List of Known Space characters
List_of_Known_Space_characters
Generalization of complex inner products
subgroup of the additive group of K. A (σ, ε)-Hermitian form is reflexive, and every reflexive σ-sesquilinear form is (σ, ε)-Hermitian for some ε. In the special
Sesquilinear_form
Tranquil, hypnotic subgenre of electronic music
to the great allegory of moving out beyond our boundaries into space, and reflexively, to the unprecedented adventures of the psyche that await within
Space_music
Creative human and cultural expression
testament to the shifting boundaries, improvisation and experimentation, reflexive nature, and self-criticism or questioning that art and its conditions
The_arts
Humor that alludes to itself
Self-referential humor, also known as self-reflexive humor, self-aware humor, or meta humor, is a type of comedic expression that—either directed toward
Self-referential_humor
X} is infinite, then C ( X ) {\displaystyle {\mathcal {C}}(X)} is not reflexive, nor is it weakly complete. The Arzelà–Ascoli theorem holds: A subset
Space of continuous functions on a compact space
Space_of_continuous_functions_on_a_compact_space
completion of it coincides with the usual completion of the space. Isbell completion (also called reflexive completion), introduced by Isbell in 1960, is in short
Completions in category theory
Completions_in_category_theory
Generalised alphabetical order
numbers to { 0 , 1 } , {\displaystyle \{0,1\},} also known as the Cantor space { 0 , 1 } ω {\displaystyle \{0,1\}^{\omega }} ) is not well-ordered; the
Lexicographic_order
Dual pair of vector spaces
appears in the theory of reflexive spaces: the Hausdorff locally convex TVS X {\displaystyle X} is said to be semi-reflexive if ( X β ′ ) ′ = X {\displaystyle
Dual_system
Relationship between elements of two sets
have are: Reflexive: for all x ∈ X , {\displaystyle x\in X,} x R x {\displaystyle xRx} . For example, ≥ {\displaystyle \geq } is a reflexive relation but
Binary_relation
Normed vector space for which the closed unit ball is strictly convex
then it is also reflexive by Milman–Pettis theorem. The following properties are equivalent to strict convexity. A normed vector space (X, || ||) is strictly
Strictly_convex_space
Partially ordered topological space
In mathematics, a partially ordered space (or pospace) is a topological space X {\displaystyle X} equipped with a closed partial order ≤ {\displaystyle
Partially_ordered_space
Barrelled space where closed and bounded subsets are compact
Schwartz space is a Montel space. Montel spaces are paracompact and normal. Semi-Montel spaces are quasi-complete and semi-reflexive while Montel spaces are
Montel_space
Locally convex topological vector space that is also a complete metric space
a Fréchet space. The strong dual of a reflexive Fréchet space is a bornological space and a Ptak space. Every Fréchet space is a Ptak space. The strong
Fréchet_space
Mathematical concept
X is a binary relation on X which is reflexive and transitive. Given a (not necessarily finite) topological space X we can define a preorder on X by x
Finite_topological_space
Property of topological spaces
connected subset of X containing both x and y. Evidently both relations are reflexive and symmetric. Moreover, if x and y are contained in a connected (respectively
Locally_connected_space
Concept in mathematics
space, do not. Spaces with Radon–Nikodym property include separable dual spaces (this is the Dunford–Pettis theorem)[citation needed] and reflexive spaces
Bochner_integral
Sentence, idea or formula that refers to itself
Retrieved 21 January 2026. Bartlett, Steven J. [James] (Ed.) (1992). Reflexivity: A Source-book in Self-reference. Amsterdam, North-Holland. (PDF). RePub
Self-reference
Vector space with a notion of nearness
locally convex space are exactly the bounded linear operators. Stereotype space: a locally convex space satisfying a variant of reflexivity condition, where
Topological_vector_space
Computational tool
separable Banach space has a Schauder basis. This was negatively answered by Per Enflo who constructed a reflexive and separable Banach space failing the approximation
Schauder_basis
reflexive Banach space is a Grothendieck space. Conversely, it is a consequence of the Eberlein–Šmulian theorem that a separable Grothendieck space X
Grothendieck_space
reference points are emancipatory forms of citizenship and the "reflexive appropriation of space". Spatial citizenship can be distinguished from traditional
Spatial_citizenship
Irish mathematician (1944–2024)
(1971), 241–288. Alencar, Raymundo; Aron, Richard M.; Dineen, Seán "A reflexive space of holomorphic functions in infinitely many variables". Proc. Amer
Seán_Dineen
Order-preserving mathematical function
of X . {\displaystyle X.} In functional analysis on a topological vector space X {\displaystyle X} , a (possibly non-linear) operator T : X → X ∗ {\displaystyle
Monotonic_function
Concept in order theory
Connected Well-founded Has joins Has meets Reflexive Irreflexive Asymmetric Total, Semiconnex Anti- reflexive Equivalence relation Y ✗ ✗ ✗ ✗ ✗ Y ✗ ✗ Preorder
Join_and_meet
Type of ordering of a set
Sufficient conditions for a binary relation R on a set X to be dense are: R is reflexive; R is coreflexive; R is quasireflexive; R is left or right Euclidean;
Dense_order
Type of topological space
locally convex spaces are also paracompact normal reflexive barrelled spaces. The strong dual spaces of both S ( R n ) {\displaystyle {\mathcal {S}}\left(\mathbb
Fréchet–Urysohn_space
N_{b}^{\prime }{\widehat {\otimes }}_{\pi }Y_{b}^{\prime }} ) is a reflexive space; Every separately continuous bilinear form on N b ′ × Y b ′ {\displaystyle
Projective_tensor_product
2007 novel by Jeanette Winterson
The Stone Gods is a novel written by Jeanette Winterson. Published in the year 2007, the novel is a post-apocalyptic, postmodern, dystopian love story
The_Stone_Gods_(novel)
1987 American comedy film by Mel Brooks
Spaceballs is a 1987 American space opera parody film co-produced, co-written, and directed by Mel Brooks. It primarily parodies the original Star Wars
Spaceballs
Type of binary relation
∈). A relation R is said to be reflexive if a R a holds for every a in the domain of the relation. Every reflexive relation on a nonempty domain has
Well-founded_relation
Functional analysis concept
operator on Hilbert space is an extension of the concept of a matrix acting on a finite-dimensional vector space; in Hilbert space, compact operators are
Compact operator on Hilbert space
Compact_operator_on_Hilbert_space
Australian animated web series
stumbles upon the exit door and enters it, going through a labyrinth of office spaces into the void beyond the circus. Caine rescues Pomni as the adventure is
The_Amazing_Digital_Circus
barrelled space. Every barrelled space is countably barrelled. However, there exist semi-reflexive countably barrelled spaces that are not barrelled. The strong
Countably_barrelled_space
American businessman (born 1964)
structure of accessing space. Malik, Tariq. "Later, Vader! Watch Blue Origin Fly 'Mannequin Skywalker' to Space and Back". Space.com. Archived from the
Jeff_Bezos
vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space whose
Ordered topological vector space
Ordered_topological_vector_space
and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. That is, for each
Browder–Minty_theorem
Space where bounded operators are continuous
The strong dual of every reflexive Fréchet space is bornological. If the strong dual of a metrizable locally convex space is separable, then it is bornological
Bornological_space
{\displaystyle \left(X,\tau _{\operatorname {O} }\right)} is reflexive. Every reflexive locally convex vector lattice is order complete and a complete
Locally_convex_vector_lattice
Set whose pairs have minima and maxima
elements has a meet or join. Pointless topology Lattice of subgroups Spectral space Invariant subspace Closure operator Abstract interpretation Subsumption
Lattice_(order)
REFLEXIVE SPACE
REFLEXIVE SPACE
Boy/Male
Hindu
Limitless space Avatar incarnation
Girl/Female
Gujarati, Hindu, Indian
Star in Space
Girl/Female
Maori
Open spaces.
Boy/Male
Arabic, Muslim, Pashtun
Battle Field; Open Space
Girl/Female
Indian, Japanese, Tamil
Space; Star
Boy/Male
Indian
Open space, Battle field
Boy/Male
Muslim
Open space, Battle field
Boy/Male
Tamil
Limitless space Avatar incarnation
Girl/Female
Biblical
Spaces, places.
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
Boy/Male
Hindu
Space
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
Antariksha | அஂதரிகà¯à®·
Boy/Male
Indian, Punjabi, Sikh
One who is Aware and Reflective
Girl/Female
Indian, Telugu
Space
Boy/Male
Hindu
Space
Surname or Lastname
English
English : habitational name from either of two places in Cheshire. It is possible that the name originally denoted a building where village assemblies were held, named in Old English as ‘meeting-house’, from (ge)mÅt ‘meeting’ + ærn ‘house’, ‘hall’. Other possibilities are that the name derives from Old English (ge)mÅt-rÅ«m ‘meeting space’, or (ge)mÅt-treum ‘assembly trees’.
Girl/Female
Indian, Telugu
Goddess of Space
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Boy/Male
Biblical
Breadth, space, extent.
Boy/Male
Hindu
Space
REFLEXIVE SPACE
REFLEXIVE SPACE
Boy/Male
Indian, Kannada
Icon; Idol; Statue; Reflection
Boy/Male
British, Christian, English, Hebrew
Famous Battle; Good-fight; To Complete
Boy/Male
Hindu
Awakened, Lord Buddha
Girl/Female
German, Swedish, Swiss
True; Faith; Sacred Wisdom
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu, Traditional
King; Ruler; Lord of Forts; Star; Part of Goddess Durga
Girl/Female
Tamil
Udipti | உதிபà¯à®¤à¯€
On fire
Boy/Male
Indian, Sanskrit
Globe; Ball
Boy/Male
Bengali, Buddhist, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
Lord of a Troop
Girl/Female
Bengali, Hindu, Indian, Kannada, Marathi, Telugu, Traditional
Daughter of a Swan
Boy/Male
Australian, French, German, Italian, Teutonic
Hard Working; Home Ruler; Industrious
REFLEXIVE SPACE
REFLEXIVE SPACE
REFLEXIVE SPACE
REFLEXIVE SPACE
REFLEXIVE SPACE
a.
Bending or turned backward; reflective; having respect to something past.
a.
Capable of exercising thought or judgment; as, reflective reason.
a.
Implying censure.
a.
Having for its direct object a pronoun which refers to the agent or subject as its antecedent; -- said of certain verbs; as, the witness perjured himself; I bethought myself. Applied also to pronouns of this class; reciprocal; reflective.
a.
Reflexive; reciprocal.
v. t. & i.
To eat to excess; -- often with a reflexive.
a.
Repletive.
a.
Throwing back images; as, a reflective mirror.
a.
Inflective.
a.
Tending to make replete; filling.
pron.
Themselves; -- used reflexively.
n.
To behave; -- with the reflexive; as, he conducted himself well.
n.
See Reflection.
a.
Not reflective.
v. t.
To carry; to conduct; -- with a reflexive pronoun.
v. t.
To accustom; -- used reflexively.
a.
Addicted to introspective or meditative habits; as, a reflective person.
n.
The state or condition of being reflected.
v. t.
To betake; to remove; -- in a reflexive use.
a.
Inflexible.