On the equivalence of McShane and Pettis integrability in non-separable Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:350

Article

Rodriguez, Jose¹ 

[1] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

关键词: Pettis integral;    McShane integral;    Scalarly null function;    Projectional resolution of the identity;    Weakly Lindelof determined Banach space;    Property (M);    Absolutely summing operator;   

DOI  :  10.1016/j.jmaa.2007.10.076

来源: Elsevier

【 摘 要 】

We show that McShane and Pettis integrability coincide for functions f : [0, 1] -> L-1 (mu), where mu is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [0, 1] -> X and an absolutely summing operator it from X to another Banach space Y such that the composition u o h : [0, 1] -> Y is not Bochner integrable; in particular, h is not McShane integrable. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free