Lebesgue-Bochner spaces, decomposable sets and strong weakly compact generation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Lajara, Sebastian²  Rodriguez, Jose¹ 

[1] Univ Murcia, Fac Informat, Dept Matemat Aplicada, Espinardo 30100, Murcia, Spain

[2] Univ Castilla La Mancha, Escuela Ingn Ind, Dept Matemat, Albacete 02071, Spain

关键词: Strongly generated Banach space;    Lebesgue-Bochner space;    Decomposable set;    Uniform Eberlein compact space;    Smoothness;   

DOI  :  10.1016/j.jmaa.2011.12.021

来源: Elsevier

【 摘 要 】

Let X be a Banach space and mu a probability measure. We prove that X is strongly reflexive (resp. super-reflexive) generated if, and only if, there exist a reflexive (resp. super-reflexive) Banach space Z and a bounded linear operator S : Z -> L-1 (mu, X) such that for each weakly compact decomposable set K subset of L-1 (mu, X) and each epsilon > 0 there is n is an element of N such that K subset of nS (B-Z) + epsilon B-L1(mu:X). This answers partially a question posed by Schluchtermann and Wheeler. Some applications are also given. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free