Banach spaces with many boundedly complete basic sequences failing PCP
Functional Analysis
2009-02-20 v1
Abstract
We prove that there exist Banach spaces not containing , failing the point of continuity property and satisfying that every semi-normalized basic sequence has a boundedly complete basic subsequence. This answers in the negative the problem of the Remark 2 in H. P. Rosenthal. "Boundedly complete weak-Cauchy sequences in Banach spaces with PCP." J. Funct. Anal. 253 (2007) 772-781.
Keywords
Cite
@article{arxiv.0902.3422,
title = {Banach spaces with many boundedly complete basic sequences failing PCP},
author = {Gines Lopez Perez},
journal= {arXiv preprint arXiv:0902.3422},
year = {2009}
}