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A Remark on non-separable solutions to the Schroeder-Bernstein Problem for Banach spaces

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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

  1. (a)

    E is isomorphic to each one of its finite codimensional subspaces.

  2. (b)

    E has no complemented Hereditarily Indecomposable subspace.

  3. (c)

    E has no complemented subspace isomorphic to its square.

  4. (d)

    E has no non-trivial divisor.

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Authors and Affiliations

  1. Department of Mathematics, IME, University of São Paulo, São Paulo, 05315-970, Brazil

    Elói Medina Galego

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  1. Elói Medina Galego
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Correspondence to Elói Medina Galego.

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Galego, E.M. A Remark on non-separable solutions to the Schroeder-Bernstein Problem for Banach spaces. Results. Math. 47, 55–60 (2005). https://doi.org/10.1007/BF03323012

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  • DOI: https://doi.org/10.1007/BF03323012

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