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

Valentin Ferenczi, and Christian Rosendal. "On the number of non-isomorphic subspaces of a Banach space." Studia Mathematica 168.3 (2005): 203-216. <http://eudml.org/doc/285362>.

@article{ValentinFerenczi2005,
abstract = {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.},
author = {Valentin Ferenczi, Christian Rosendal},
journal = {Studia Mathematica},
keywords = {subspaces of Banach spaces; unconditional basis; homogeneous Banach spaces; hereditarily indecomposable Banach spaces},
language = {eng},
number = {3},
pages = {203-216},
title = {On the number of non-isomorphic subspaces of a Banach space},
url = {http://eudml.org/doc/285362},
volume = {168},
year = {2005},
}

TY - JOUR
AU - Valentin Ferenczi
AU - Christian Rosendal
TI - On the number of non-isomorphic subspaces of a Banach space
JO - Studia Mathematica
PY - 2005
VL - 168
IS - 3
SP - 203
EP - 216
AB - 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.
LA - eng
KW - subspaces of Banach spaces; unconditional basis; homogeneous Banach spaces; hereditarily indecomposable Banach spaces
UR - http://eudml.org/doc/285362
ER -