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