The Schroeder-Bernstein index for Banach spaces

Elói Medina Galego. "The Schroeder-Bernstein index for Banach spaces." Studia Mathematica 164.1 (2004): 29-38. <http://eudml.org/doc/285373>.

@article{ElóiMedinaGalego2004,
abstract = {In relation to some Banach spaces recently constructed by W. T. Gowers and B. Maurey, we introduce the notion of Schroeder-Bernstein index SBi(X) for every Banach space X. This index is related to complemented subspaces of X which contain some complemented copy of X. Then we establish the existence of a Banach space E which is not isomorphic to Eⁿ for every n ∈ ℕ, n ≥ 2, but has a complemented subspace isomorphic to E². In particular, SBi(E) is uncountable. The construction of E follows the approach given in 1996 by W. T. Gowers to obtain the first solution to the Schroeder-Bernstein Problem for Banach spaces.},
author = {Elói Medina Galego},
journal = {Studia Mathematica},
keywords = {Schröder-Bernstein problem; complemented subspace; square of a Banach space},
language = {eng},
number = {1},
pages = {29-38},
title = {The Schroeder-Bernstein index for Banach spaces},
url = {http://eudml.org/doc/285373},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Elói Medina Galego
TI - The Schroeder-Bernstein index for Banach spaces
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 1
SP - 29
EP - 38
AB - In relation to some Banach spaces recently constructed by W. T. Gowers and B. Maurey, we introduce the notion of Schroeder-Bernstein index SBi(X) for every Banach space X. This index is related to complemented subspaces of X which contain some complemented copy of X. Then we establish the existence of a Banach space E which is not isomorphic to Eⁿ for every n ∈ ℕ, n ≥ 2, but has a complemented subspace isomorphic to E². In particular, SBi(E) is uncountable. The construction of E follows the approach given in 1996 by W. T. Gowers to obtain the first solution to the Schroeder-Bernstein Problem for Banach spaces.
LA - eng
KW - Schröder-Bernstein problem; complemented subspace; square of a Banach space
UR - http://eudml.org/doc/285373
ER -