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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
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
spaces were ℓ p and c0. The dual space T is not minimal. The space T* is polynomially reflexive. The symmetric Tsirelson space S(T) is polynomially reflexive
Tsirelson_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
Vector space of infinite sequences
\ell ^{q}} is that it is not polynomially reflexive. For p ∈ [ 1 , ∞ ] {\displaystyle p\in [1,\infty ]} , the spaces ℓ p {\displaystyle \textstyle
Sequence_space
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
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)
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
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
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
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
French mathematician
of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier proved that super-reflexive Banach spaces can be renormed
Gilles_Pisier
Swedish mathematician and concert pianist
unless the segment is short. In 1972 Enflo proved that "every super-reflexive Banach space admits an equivalent uniformly convex norm". With one paper, which
Per_Enflo
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
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)
Field in logic and theoretical computer science
system. A proof system with a polynomial-time prover is automatable. A proof system P {\displaystyle P} is polynomially bounded (p-bounded) iff for any
Proof_complexity
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)
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
Generalised alphabetical order
considering polynomials, the order of the terms does not matter in general, as the addition is commutative. However, some algorithms, such as polynomial long
Lexicographic_order
for multivariable calculus over spaces of matrices Umbral calculus, the combinatorics of certain operations on polynomials Vector calculus (also called vector
List_of_formal_systems
Finiteness of sets of forbidden graph minors
undirected graphs, as it obeys the three axioms of partial orders: it is reflexive (every graph is a minor of itself), transitive (a minor of a minor of
Robertson–Seymour_theorem
Construction in functional analysis, useful to solve differential equations
since reflexivity no longer holds. Hilbert spaces are Banach spaces, so the above discussion applies to bounded operators on Hilbert spaces as well
Decomposition of spectrum (functional analysis)
Decomposition_of_spectrum_(functional_analysis)
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
Algebraic object with an ordered structure
space Ordered vector space – Vector space with a partial order Partially ordered ring – Ring with a compatible partial order Partially ordered space –
Ordered_field
Knot that bounds an embedded disk in 4-space
addition the orientation is reversed. The relationship ′concordant′ is reflexive because K ♯ − K {\displaystyle K\sharp -K} is slice for every knot K {\displaystyle
Slice_knot
a binary relation on pairs of elements of S {\displaystyle S} that is reflexive (for all x ∈ S {\displaystyle x\in S} , x ≤ x {\displaystyle x\leq x}
Order_polytope
Generalizations of codimension-1 subvarieties of algebraic varieties
isomorphism classes of rank-one reflexive sheaves on X. Let k be a field, and let n be a positive integer. Since the polynomial ring k[x1, ..., xn] is a unique
Divisor_(algebraic_geometry)
Topics referred to by the same term
arising in electronics Lambda calculus, a formulation of the theory of reflexive functions that has deep connections to computational theory Kappa calculus
Calculus_(disambiguation)
Maximal subgraph whose vertices can reach each other
vertices and edges). Reachability is an equivalence relation, since: It is reflexive: There is a trivial path of length zero from any vertex to itself. It
Component_(graph_theory)
Hierarchy of complexity classes for formulas defining sets
arithmetically reducible to Y. The relation X ≤ A Y {\displaystyle X\leq _{A}Y} is reflexive and transitive, and thus the relation ≡ A {\displaystyle \equiv _{A}}
Arithmetical_hierarchy
Mathematical ordering of a partial order
sets is a linear extension of their product order. A partial order is a reflexive, transitive and antisymmetric relation. Given any partial orders ≤ {\displaystyle
Linear_extension
{\displaystyle B_{n}} denotes the n {\displaystyle n} -th Bell polynomial. Each Bell polynomial is a finite sum of monomials of the form ∏ i = 1 n ( g ( i
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
Type of Turing reduction
for example that the reduction function is computable in polynomial time, logarithmic space, by A C 0 {\displaystyle AC_{0}} or N C 0 {\displaystyle NC_{0}}
Many-one_reduction
Transformation of one computational problem to another
corresponds to many-one reduction. Reducibility is a preordering, that is, a reflexive and transitive relation, on P(N)×P(N), where P(N) is the power set of
Reduction_(complexity)
On chains and antichains in partial orders
bipartite matching allows the width of any partial order to be computed in polynomial time. More precisely, n-element partial orders of width k can be recognized
Dilworth's_theorem
Algebraic ring without a multiplicative identity
idempotent is 0, the only nilpotent is 0, and the only element with a reflexive inverse is 0. The direct sum T = ⨁ i = 1 ∞ Z / 5 Z {\textstyle {\mathcal
Rng_(algebra)
Overview of and topical guide to discrete mathematics
descriptions of redirect targets Reflexive relation – Binary relation that relates every element to itself Reflexive property of equality – Basic notion
Outline of discrete mathematics
Outline_of_discrete_mathematics
String rewriting system
when e.g. guaranteeing termination of the string rewriting rules within polynomially many steps in the input size), or equivalently a Quantum Turing machine
Semi-Thue_system
Uniqueness of countable dense linear orders
element. This is different from the concept of a bounded set in a metric space. For instance, the open interval (0,1) is unbounded as an ordered set, even
Cantor's_isomorphism_theorem
sufficient operator Symmetric Boolean function Symmetric difference Zhegalkin polynomial Boolean domain Complete Boolean algebra Interior algebra Two-element Boolean
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Generalization of vector bundles
as the Riemann–Roch theorem. Picard group Divisor (algebraic geometry) Reflexive sheaf Quot scheme Twisted sheaf Essentially finite vector bundle Bundle
Coherent_sheaf
Mathematical relation making a non-equal comparison
which is reflexive, antisymmetric, and transitive. That is, for all a, b, and c in P, it must satisfy the three following clauses: a ≤ a (reflexivity) if a
Inequality_(mathematics)
Particular correspondence between two partially ordered sets
(trivial) Galois connection, as follows. Because the equality relation is reflexive, transitive and antisymmetric, it is, trivially, a partial order, making
Galois_connection
Subset of incomparable elements
its size, the width of a given partially ordered set) can be found in polynomial time. Counting the number of antichains in a given partially ordered set
Antichain
{O}}_{X}}{\mathcal {O}}_{X}(D).} If D is a Weil divisor and F is reflexive, then one replaces F(D) by its reflexive hull (and calls the result still F(D)). |D| The complete
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
algebra is a way of writing in it in terms of polynomial subalgebras. reflexive A module M is reflexive if the canonical map M → M ∗ ∗ , m ↦ ⟨ ⋅ , m ⟩
Glossary of commutative algebra
Glossary_of_commutative_algebra
Graph linking pairs of comparable elements in a partial order
coloring and the independent set problem, can be solved for these graphs in polynomial time. Bound graph, a different graph defined from a partial order Golumbic
Comparability_graph
Branch of mathematics that studies algebraic structures
Finitely-presented module Finitely related module Algebraically compact module Reflexive module Composition series Length of a module Structure theorem for finitely
List of abstract algebra topics
List_of_abstract_algebra_topics
Algebraic structure used in logic
1 p.78. Statman, R. (1979). "Intuitionistic propositional logic is polynomial-space complete". Theoretical Comput. Sci. 9: 67–72. doi:10.1016/0304-3975(79)90006-9
Heyting_algebra
Most widely known generalized inverse of a matrix
A + = A + {\textstyle A^{+}AA^{+}=A^{+}} , it is called a generalized reflexive inverse. Generalized inverses always exist but are not in general unique
Moore–Penrose_inverse
In mathematics, invertible homomorphism
f(v))\quad {\text{ if and only if }}\quad \operatorname {R} (u,v)} S is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, total
Isomorphism
extensions of an arbitrary partial order is #P-complete, it may be solved in polynomial time for series-parallel partial orders. Specifically, if L(P) denotes
Series-parallel_partial_order
materially equivalent. equivalence relation A binary relation that is reflexive, symmetric, and transitive, indicating that elements it relates are in
Glossary_of_logic
objects are substructures of themselves (that is, the relationship is reflexive), then the qualification proper requires the objects to be different.
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Vector bundles theorem
Bando–Siu to singular holomorphic vector bundles, otherwise known as reflexive sheaves. This involves defining a notion of singular Hermite–Einstein
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Set of eigenvalues of a matrix
{Ran} (T^{*}-{\bar {\lambda }}I)} can not be dense. Furthermore, if X is reflexive, we have σ r ( T ∗ ) ¯ ⊂ σ p ( T ) {\displaystyle {\overline {\sigma _{\mathrm
Spectrum (functional analysis)
Spectrum_(functional_analysis)
Mathematics of convex functions and sets
semicontinuity, and reflexivity assumptions, such as those in the direct methods in the calculus of variations. For example, in a reflexive Banach space, closed bounded
Convex_analysis
4 September 2022. Retrieved 4 September 2022. Original Space Academy GX-1 box Original Space Madness packaging Original Spectre VR box Spy Fox in Cheese
List_of_Mac_games
Algebraic ring that need not have additive negative elements
star operation is actually the reflexive and transitive closure of R {\displaystyle R} (that is, the smallest reflexive and transitive binary relation
Semiring
Size of a set in mathematics
satisfying the same three basic properties as equality: reflexivity, symmetry, and transitivity. Reflexivity, the property that every set has the same cardinality
Cardinality
Polygon through a set of points
Joseph S. B.; Noy, Marc; Sacristán, Vera; Sethia, Saurabh (2003), "On the reflexivity of point sets", in Aronov, Boris; Basu, Saugata; Pach, János; Sharir
Polygonalization
Property of a mathematical matrix
define a non-strict partial order B ⪰ A {\displaystyle B\succeq A} that is reflexive, antisymmetric, and transitive; It is not a total order, however, as B
Definite_matrix
Basic concepts of algebra
flipped. By definition, equality is an equivalence relation, meaning it is reflexive (i.e. b = b {\displaystyle b=b} ), symmetric (i.e. if a = b {\displaystyle
Elementary_algebra
Model to describe distributed systems
{\displaystyle {\overset {*}{\underset {G}{\longrightarrow }}}} is the reflexive transitive closure of ⟶ G {\displaystyle {\underset {G}{\longrightarrow
Petri_net
Isometric subgraph of a hypercube
) {\displaystyle d(x,u)+d(y,v)\not =d(x,v)+d(y,u)} . This relation is reflexive and symmetric, but in general it is not transitive. Winkler showed that
Partial_cube
Family of knowledge representation languages
three sublanguages (known as profiles): OWL2 EL is a fragment that has polynomial time reasoning complexity. It is based on the description logic E L {\displaystyle
Web_Ontology_Language
Operation that pairs a left and a right R-module into an abelian group
isomorphism if E is a free module of finite rank. In general, E is called a reflexive module if the canonical homomorphism is an isomorphism. We denote the
Tensor_product_of_modules
Quality of zero being an even number
y) is even. Here, the evenness of zero is directly manifested as the reflexivity of the binary relation ~. There are only two cosets of this subgroup—the
Parity_of_zero
Process of changing beliefs to take into account a new piece of information
entrenchments, systems of spheres, and preference relations. The latter are reflexive, transitive, and total relations over the set of models. Each revision
Belief_revision
Branch of type theory
subtyping ( ≤ ) {\displaystyle (\leq )} is defined as the smallest preorder (reflexive and transitive relation) over intersection types satisfying the following
Intersection_type_discipline
Tool for proving a logical formula
amount of space, as the breadth of the tree can grow exponentially. A method that may visit some nodes more than once but works in polynomial space is to
Method_of_analytic_tableaux
continuity. For general k, it can also be verified directly: The relation is reflexive since (a,0) is quasi-invertible and a0 = a. The relation is symmetric
Mutation_(Jordan_algebra)
Axiomatization of arithmetic
{\displaystyle t} , the equality t = t {\displaystyle t=t} is true by reflexivity and a proposition P {\displaystyle P} is equivalent to ( t = t ) → P
Heyting_arithmetic
POLYNOMIALLY REFLEXIVE-SPACE
POLYNOMIALLY REFLEXIVE-SPACE
Boy/Male
Indian
Open space, Battle field
Boy/Male
Arabic, Muslim, Pashtun
Battle Field; Open Space
Boy/Male
Indian, Punjabi, Sikh
One who is Aware and Reflective
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.
Girl/Female
Gujarati, Hindu, Indian
Star in Space
Girl/Female
Indian, Telugu
Space
Girl/Female
Indian, Telugu
Goddess of Space
Boy/Male
Biblical
Breadth, space, extent.
Boy/Male
Hindu
Space
Boy/Male
Hindu
Space
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Boy/Male
Tamil
Limitless space Avatar incarnation
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
Antariksha | அஂதரிகà¯à®·
Boy/Male
Hindu
Space
Girl/Female
Maori
Open spaces.
Boy/Male
Hindu
Limitless space Avatar incarnation
Boy/Male
Muslim
Open space, Battle field
Girl/Female
Indian, Japanese, Tamil
Space; Star
Girl/Female
Biblical
Spaces, places.
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’.
POLYNOMIALLY REFLEXIVE-SPACE
POLYNOMIALLY REFLEXIVE-SPACE
Girl/Female
Hindu
A shout of Joy, Rejoicing
Girl/Female
Arabic, Muslim
Respect; Honour
Boy/Male
Muslim
Respect
Male
English
Short form of English Douglas, DOUG means "black stream."
Boy/Male
Tamil
Vishwajeet | விஷà¯à®µà®œà¯€à®¤
Conqueror of the world, Who has won the world
Girl/Female
Arabic, Gujarati, Hindu, Indian, Muslim
Goodluck
Boy/Male
Sikh
Incarnate, Holy incarnation
Boy/Male
Australian, British, Christian, English, French, Gaelic, Greek, Scottish
Variant of Alexander; Defender of Mankind
Surname or Lastname
English
English : nickname from Middle English sparewe ‘sparrow’, perhaps for a small, chirpy person, or else for someone bearing some fancied physical resemblance to a sparrow.
Girl/Female
Hindu
Graceful
POLYNOMIALLY REFLEXIVE-SPACE
POLYNOMIALLY REFLEXIVE-SPACE
POLYNOMIALLY REFLEXIVE-SPACE
POLYNOMIALLY REFLEXIVE-SPACE
POLYNOMIALLY REFLEXIVE-SPACE
n.
A polynomial name or term.
pron.
Themselves; -- used reflexively.
v. t.
To accustom; -- used reflexively.
v. t.
To betake; to remove; -- in a reflexive use.
n.
To behave; -- with the reflexive; as, he conducted himself well.
a.
Not reflective.
v. t. & i.
To eat to excess; -- often with a reflexive.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
a.
Addicted to introspective or meditative habits; as, a reflective person.
v. t.
To carry; to conduct; -- with a reflexive pronoun.
a.
Repletive.
a.
Throwing back images; as, a reflective mirror.
a.
Reflexive; reciprocal.
n.
An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
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.
n. & a.
Same as Polynomial.
a.
Bending or turned backward; reflective; having respect to something past.
a.
Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
a.
Implying censure.
a.
Capable of exercising thought or judgment; as, reflective reason.