Some results about the Schroeder-Bernstein Property for separable Banach spaces
Valentin Ferenczi, 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 20. 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.
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