1991/10/09 by Peter Ørno, Ørno, Peter · 1 citation
Mathematics · #46B #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.math/9201233
openalex publication_date 1991/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Banach space X is reflexive if the Mackey topology τ(X^*,X) on X^* agrees with the norm topology on X^*. Borwein [B] calls a Banach space X \it sequentially reflexive\/ provided that every τ(X^*,X) convergent \it sequence\/ in X^* is norm convergent. The main result in [B] is that X is sequentially reflexive if every separable subspace of X has separable dual, and Borwein asks for a characterization of sequentially reflexive spaces. Here we answer that question by proving \proclaim Theorem. \sl A Banach space X is sequentially reflexive if and only if ℓ1 is not isomorphic to a subspace of X.