reflexive space

This should not be confused with a reflexive space.

As a consequence ℓ is a reflexive space.

Every closed subspace of a reflexive space is reflexive.

The upper-θ and lower-θ methods do not coincide in general, but they do for reflexive spaces.

Weak compactness of the unit ball provides a tool for finding solutions in reflexive spaces to certain optimization problems.

This makes polynomially reflexive spaces rare.

A bounded linear operator between two Banach spaces is weakly compact if and only if it factors through a reflexive space.

In fact, this result also extends to the case of strongly continuous one-parameter semigroup of contractive operators on a reflexive space.

For example, every convex continuous function on the unit ball B of a reflexive space attains its minimum at some point in B.

A topological vector space that is canonically isomorphic to its bidual is called reflexive space.

A generalization which has some of the properties of reflexive spaces and includes many spaces of practical importance is the concept of Grothendieck space.

Spaces with Radon-Nikodym property include separable dual spaces (this is the Dunford-Pettis theorem) and reflexive spaces, which include, in particular, Hilbert spaces.

In mathematics, a polynomially reflexive space is a Banach space X, on which the space of all polynomials in each degree is a reflexive space.

In a reflexive space the left and right radicals agree and are termed the kernel or the radical of the bilinear form: the subspace of all vectors orthogonal with every other vector.

Among all locally convex spaces (even among all Banach spaces) used in functional analysis the class of reflexive spaces is too narrow to represent a self-sufficient category in any sense.

As a special case of the preceding result, when X is a reflexive space over R, every continuous linear functional f in X ' attains its maximum ǁf ǁ on the unit ball of X. The following theorem of Robert C. James provides a converse statement.

One of their main advantages is that they offer a way to deal with the fact that the Sobolev space W is not a reflexive space; since W is not reflexive, it is not always true that a bounded sequence has a weakly convergent subsequence, which is a desideratum in many applications.