
TL;DR
This paper investigates the properties of coreflexive Banach spaces, characterizing their stability under certain operations and their behavior in related function spaces, with implications for the structure of non-reflexive spaces.
Contribution
It provides new characterizations of coreflexive spaces, proves their stability under $oldsymbol{ extstyle ext{l}^{p}}$-sums, and explores their behavior in Bochner $L^{p}$-spaces.
Findings
Coreflexive spaces are stable under $ ext{l}^{p}$-sums for $1<p< ext{infty}$.
A space $X$ is coreflexive iff every separable subspace is coreflexive under certain conditions.
$L^{p}( ext{mu},X)$ is coreflexive if $X$ is coreflexive with separable $X^{**}/X$.
Abstract
In this paper, we study non-reflexive Banach spaces for which the quotient space is reflexive. Such spaces were first introduced by James R.~Clark, where they were called coreflexive spaces. We show that a space is coreflexive if and only if every separable subspace is coreflexive, provided that is w-sequently dense in its bidual . We show that coreflexive spaces are stable under -sum for . We show that if is a coreflexive space such that is separable, then the space of Bochner -integrable functions, is coreflexive for . We conclude by providing an alternative proof of the fact, in a quasi-reflexive space , w-PC's of the unit ball continue to have the same property in all the higher even-order dual unit balls of .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
