Super WCG Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:439

Article

Raja, M.¹ 

[1] Univ Murcia, Dept Matemat, Campus Espinardo, E-30100 Murcia, Spain

关键词: Super weak compactness;    Uniformly Gateaux smoothness;    Strongly generated Banach space;   

DOI  :  10.1016/j.jmaa.2016.02.057

来源: Elsevier

【 摘 要 】

A Banach space X admits an equivalent strongly uniformly Gateaux smooth norm if and only if it contains the dense range of a super weakly compact operator, which is equivalent to say that X is generated by a convex super weakly compact set. Moreover, if X is strongly generated by a convex super weakly compact set, then there is an equivalent norm on X such that its restriction to any reflexive subspace of X is both uniformly convex and uniformly Frechet smooth. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free