On the number of non-isomorphic subspaces of a Banach space

Valentin Ferenczi ; Christian Rosendal

Studia Mathematica, Tome 166 (2005), p. 203-216 / Harvested from The Polish Digital Mathematics Library

Résumé

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let be a Banach space with an unconditional basis $(e_{i})_{i∈ℕ}$; then either there exists a perfect set P of infinite subsets of ℕ such that for any two distinct A,B ∈ P, $[e_{i}]_{i∈A} ≇ [e_{i}]_{i∈B}$, or for a residual set of infinite subsets A of ℕ, $[e_{i}]_{i∈A}$ is isomorphic to , and in that case, is isomorphic to its square, to its hyperplanes, uniformly isomorphic to $ ⊕ [e_{i}]_{i∈D}$ for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition into uniformly isomorphic copies of itself.

Détail

Publié le : 2005-01-01

Zbl 1082.46008

EUDML-ID : urn:eudml:doc:285362