Sentence examples for be a closed subspace from inspiring English sources

Let Y be a closed subspace of Lp, where μ is an arbitrary measure and 1 < p < ∞.

Let X be a closed subspace of a Banach space Y and J be the inclusion map.

Let X be a Banach space and let Y be a closed subspace of a Banach space Z.

Let be a closed subspace of.

Let (Ysubset X) be a closed subspace.

Let M be a closed subspace of X.

We introduce a natural Banach algebra, which is a closed subspace of ⟨A∗A⟩∗ but equipped with a distinct multiplication.

Given a Banach space X and an operator T∈L X), an almost-invariant half-space (AIHS) is a closed subspace Y satisfying TY⊆Y+F for some finite-dimensional subspace F and dim⁡(Y)= dim⁡(X/Y)="∞.

Furthermore π is Naimark related to a representation on a reflexive Fréchet space which is a closed subspace of C(G) of the form span {L g)φ | g ∈ G} where φ is a χ-spherical function.

Read found an equivalent norm ⦀⋅⦀ on c0 such that (c0,⦀⋅⦀) contains no proximinal subspaces of codimension 2. Our result is obtained through a study of the relation between the following two sentences, in which X is a Banach space and Y⊂X is a closed subspace: (A)Y is proximinal in X, and (B Y⊥ consists of norm-attaining functionals.

Lemma 4.9. is a closed subspace of.