Incomparable, non-isomorphic and minimal Banach spaces

Christian Rosendal. "Incomparable, non-isomorphic and minimal Banach spaces." Fundamenta Mathematicae 183.3 (2004): 253-274. <http://eudml.org/doc/283048>.

@article{ChristianRosendal2004,
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 E₀ 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.},
author = {Christian Rosendal},
journal = {Fundamenta Mathematicae},
keywords = {minimal Banach space; incomparable Banach spaces; Borel reducibility},
language = {eng},
number = {3},
pages = {253-274},
title = {Incomparable, non-isomorphic and minimal Banach spaces},
url = {http://eudml.org/doc/283048},
volume = {183},
year = {2004},
}

TY - JOUR
AU - Christian Rosendal
TI - Incomparable, non-isomorphic and minimal Banach spaces
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 3
SP - 253
EP - 274
AB - 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 E₀ 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.
LA - eng
KW - minimal Banach space; incomparable Banach spaces; Borel reducibility
UR - http://eudml.org/doc/283048
ER -