English

Incomparable, non isomorphic and minimal Banach spaces

Functional Analysis 2007-05-23 v1 Logic

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 E0E_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 has an isomorphically homogeneous subsequence.

Keywords

Cite

@article{arxiv.math/0407111,
  title  = {Incomparable, non isomorphic and minimal Banach spaces},
  author = {Christian Rosendal},
  journal= {arXiv preprint arXiv:math/0407111},
  year   = {2007}
}