Banach spaces with many boundedly complete basic sequences failing PCP

Details Banach spaces with many boundedly complete basic sequences failing PCP Banach spaces with many boundedly complete basic sequences failing PCP

2009-02-19

arxiv.org/abs/0902.3422v1

Mathematics

Functional Analysis

Scientific paper

We prove that there exist Banach spaces not containing $\ell_1$, 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.

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