Banach spaces with many boundedly complete basic sequences failing PCP
classification
🧮 math.FA
keywords
banachbasicboundedlycompletespacesfailingsequencesanal
read the original abstract
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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.