[Banach] Abstract of a paper by Gines Lopez Perez

This is an announcement for the paper "Banach spaces with many boundedly complete basic sequences failing PCP" by Gines Lopez Perez.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20; 46B22

The source file(s), pcp.tex: 25505 bytes, is(are) stored in gzipped form as 0902.3422.gz with size 8kb. The corresponding postcript file has gzipped size 72kb.

Submitted from: glopezp@ugr.es

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