[Banach] Abstract of a paper by Valentin Ferenczi and Eloi Medina Galego

[Dale Alspach]

This is an announcement for the paper "Some results about the
Schroeder-Bernstein Property for separable Banach spaces" by Valentin
Ferenczi and Eloi Medina Galego.


Abstract: We construct a continuum of mutually non-isomorphic separable
Banach spaces which are complemented in each other. Consequently, the
Schroeder-Bernstein Index of any of these spaces is $2^{\aleph_0}$. Our
construction is based on a Banach space introduced by W. T. Gowers
and B. Maurey in 1997. We also use classical descriptive set theory
methods, as in some work of V. Ferenczi and C.  Rosendal, to improve some
results of P. G. Casazza and of N. J. Kalton on the Schroeder-Bernstein
Property for spaces with an unconditional finite-dimensional Schauder
decomposition.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B03, 46B20

Remarks: 25 pages

The source file(s), ferenczigalegoSB.tex: 74499 bytes, is(are) stored in
gzipped form as 0406479.gz with size 22kb. The corresponding postcript
file has gzipped size 87kb.

Submitted from: eloi at ime.usp.br

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 http://front.math.ucdavis.edu/math.FA/0406479

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 http://arXiv.org/abs/math.FA/0406479

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