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@ime.usp.br
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