A Remark on non-separable solutions to the Schroeder-Bernstein Problem for Banach spaces |
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Authors: | Elói Medina Galego |
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Institution: | 1. Department of Mathematics, IME, University of S?o Paulo, S?o Paulo, 05315-970, Brazil
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Abstract: | We show that the geometric structure of Banach spaces which are solutions to the Schroeder-Bernstein Problem is very complex. More precisely, we prove that there exists a non-separable solution E to this problem such that - E is isomorphic to each one of its finite codimensional subspaces.
- E has no complemented Hereditarily Indecomposable subspace.
- E has no complemented subspace isomorphic to its square.
- E has no non-trivial divisor.
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