English

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 1\ell_1, 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}
}
R2 v1 2026-06-21T12:13:30.358Z