areas of mathematics, the strong dual space of a topological vector space (TVS) X {\displaystyle X} is the continuous dual space X ′ {\displaystyle X^{\prime...

In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms...

(which is the strong dual of the strong dual of X {\displaystyle X} ) is a homeomorphism (or equivalently, a TVS isomorphism). A normed space is reflexive...

metrizable strong dual spaces. Every normed space can be isometrically embedded onto a dense vector subspace of some Banach space, where this Banach space is...

instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and...

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 bidual...

strong dual space are also: complete Hausdorff locally convex spaces, nuclear Montel spaces, It is known that in the dual space of any Montel space,...

topology – Dual space topology of uniform convergence on some sub-collection of bounded subsets Reductive dual pair Strong dual space – Continuous dual space endowed...

the origin. the strong dual space X b ′ {\displaystyle X_{b}^{\prime }} of X {\displaystyle X} is normable. the strong dual space X b ′ {\displaystyle X_{b}^{\prime...

Hausdorff locally convex TVS. The strong dual space of C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)} is called the space of distributions on U {\displaystyle...

\ell ^{p}} space with the largest p {\displaystyle p} . This space is the strong dual space of ℓ 1 {\displaystyle \ell ^{1}} : indeed, every x ∈ ℓ ∞ {\displaystyle...

values of the dual and primal LPs. The strong duality theorem states that, moreover, if the primal has an optimal solution then the dual has an optimal...

initial topology of a topological vector space (such as a normed vector space) with respect to its continuous dual. The remainder of this article will deal...

distinguished spaces are topological vector spaces (TVSs) having the property that weak-* bounded subsets of their biduals (that is, the strong dual space of their...

space C c ∞ {\displaystyle C_{c}^{\infty }} with L 2 {\displaystyle L^{2}} (which is a reflexive space that is even isomorphic to its own strong dual...

a DF-space. The strong dual of a DF-space is a Fréchet space. The strong dual of a reflexive Fréchet space is a bornological space. The strong bidual...

character on the dual. This is strongly analogous to the canonical isomorphism between a finite-dimensional vector space and its double dual, V ≅ V ∗ ∗ {\displaystyle...

semi-reflexive space is a locally convex topological vector space (TVS) X such that the canonical evaluation map from X into its bidual (which is the strong dual of...

is the continuous dual space of X {\displaystyle X} endowed with the strong dual topology). A locally convex topological vector space (TVS) X {\displaystyle...

nuclear Montel bornological barrelled Mackey space; the same is true of its strong dual space (that is, the space of all distributions with its usual topology)...

problems, the duality gap is zero under a constraint qualification condition. This fact is called strong duality. Usually the term "dual problem" refers...

C^{\infty }(U),} as well as the strong dual spaces of both these of spaces, are complete nuclear Montel ultrabornological spaces, which implies that all four...

the dual norm is a measure of size for a continuous linear function defined on a normed vector space. Let X {\displaystyle X} be a normed vector space with...

bornological strong duals. The strong dual of every reflexive Fréchet space is bornological. If the strong dual of a metrizable locally convex space is separable...

Fréchet space if and only if all Xi are normable. Thus the strong dual space of an LF-space is a Fréchet space if and only if it is an LB-space. A typical...

"U-duality (symmetry) group" of M-theory as defined on a particular background space (topological manifold). This is the union of all the S-duality and...

the Gelfand dual of A (not to be confused with the dual A' of the Banach space A). In particular, suppose X is a compact Hausdorff space. Then there is...

distinguished spaces, DF-spaces, and σ {\displaystyle \sigma } -barrelled spaces that are not quasibarrelled. The strong dual space X b ′ {\displaystyle X_{b}^{\prime...

discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each pair...

s=\left(s_{n}\right)_{n=1}^{\infty }\in K} . Lp space Tsirelson space beta-dual space Orlicz sequence space Hilbert space Jarchow 1981, pp. 129–130. Debnath, Lokenath;...