Abstract of a paper by Valentin Ferenczi
This is an announcement for the paper "A Banach space dichotomy for quotients of subspaces" by Valentin Ferenczi. Abstract: A Banach space $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable (QHI) property if $X/Y$ is hereditarily indecomposable (HI) for any infinite codimensional subspace $Y$ with a successive finite-dimensional decomposition on the basis of $X$. A reflexive space with the restricted QHI property is in particular HI, has HI dual, and is saturated with subspaces which are HI and have HI dual. The following dichotomy theorem is proved: any infinite dimensional Banach space contains a quotient of subspace which either has an unconditional basis, or has the restricted QHI property. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03, 46B10 Remarks: 25 pages The source file(s), dichotomyferenczi0306.tex: 67293 bytes, is(are) stored in gzipped form as 0603188.gz with size 20kb. The corresponding postcript file has gzipped size 78kb. Submitted from: ferenczi@ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0603188 or http://arXiv.org/abs/math.FA/0603188 or by email in unzipped form by transmitting an empty message with subject line uget 0603188 or in gzipped form by using subject line get 0603188 to: math@arXiv.org.
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Dale Alspach