Incomparable, non-isomorphic and minimal Banach spaces
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.
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
Affiliations des auteurs :
Christian Rosendal 1
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author = {Christian Rosendal},
title = {Incomparable, non-isomorphic and minimal {Banach} spaces},
journal = {Fundamenta Mathematicae},
pages = {253--274},
publisher = {mathdoc},
volume = {183},
number = {3},
year = {2004},
doi = {10.4064/fm183-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm183-3-5/}
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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
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