Incomparable, non-isomorphic and minimal Banach spaces

Volume 183 / 2004

Christian Rosendal Fundamenta Mathematicae 183 (2004), 253-274 MSC: Primary 46B03; Secondary 03E15. DOI: 10.4064/fm183-3-5

Abstract

A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if $E_0$ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes, and the unconditional basis has an isomorphically homogeneous subsequence.

Authors

  • Christian RosendalMathematics 253-37
    California Institute of Technology
    Pasadena, CA 91125, U.S.A.
    e-mail

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