Incomparable, non-isomorphic and minimal Banach spaces
Tom 183 / 2004
Fundamenta Mathematicae 183 (2004), 253-274 MSC: Primary 46B03; Secondary 03E15. DOI: 10.4064/fm183-3-5
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.