location:  Publications → journals → CJM
Abstract view

# Some Results on the Schroeder--Bernstein Property for Separable Banach Spaces

Published:2007-02-01
Printed: Feb 2007
• Valentin Ferenczi
• Elói Medina Galego
 Format: HTML LaTeX MathJax PDF PostScript

## 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 the first author 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.
 Keywords: complemented subspaces, Schroeder-Bernstein property
 MSC Classifications: 46B03 - Isomorphic theory (including renorming) of Banach spaces 46B20 - Geometry and structure of normed linear spaces

 top of page | contact us | privacy | site map |