Geodesic
Incomparable, non-isomorphic and minimal Banach spaces
Christian Rosendal1
1 Mathematics 253-37 California Institute of Technology Pasadena, CA 91125, U.S.A.
Fundamenta Mathematicae, Tome 183 (2004) no. 3, pp. 253-274.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm183-3-5
Keywords: banach space contains either minimal subspace continuum incomparable subspaces general structure results analytic equivalence relations applied context banach spaces does reduce isomorphism subspaces space particular subspaces space admit classification isomorphism real numbers subspace unconditional basis isomorphic its square hyperplanes unconditional basis has isomorphically homogeneous subsequence

Christian Rosendal 1

1 Mathematics 253-37 California Institute of Technology Pasadena, CA 91125, U.S.A. 
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Christian Rosendal. Incomparable, non-isomorphic and minimal Banach spaces. Fundamenta Mathematicae, Tome 183 (2004) no. 3, pp. 253-274. doi : 10.4064/fm183-3-5. http://geodesic.mathdoc.fr/articles/10.4064/fm183-3-5/

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