The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, and Jesús Suárez. "The structure of Lindenstrauss-Pełczyński spaces." Studia Mathematica 194.2 (2009): 105-115. <http://eudml.org/doc/285193>.

@article{JesúsM2009,
abstract = {Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative answer to a problem posed by Lindenstrauss and Pełczyński [J. Funct. Anal. 8 (1971)]. We show that the class of ℒ-spaces does not have the 3-space property, which corrects a theorem in an earlier paper of the authors [Studia Math. 174 (2006)]. We then solve a problem in that paper showing that $ℒ_\{∞\}$ spaces not containing l₁ are not necessarily ℒ-spaces.},
author = {Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez},
journal = {Studia Mathematica},
keywords = {extension of operators; exact sequence of Banach spaces; three-space property},
language = {eng},
number = {2},
pages = {105-115},
title = {The structure of Lindenstrauss-Pełczyński spaces},
url = {http://eudml.org/doc/285193},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Jesús M. F. Castillo
AU - Yolanda Moreno
AU - Jesús Suárez
TI - The structure of Lindenstrauss-Pełczyński spaces
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 2
SP - 105
EP - 115
AB - Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative answer to a problem posed by Lindenstrauss and Pełczyński [J. Funct. Anal. 8 (1971)]. We show that the class of ℒ-spaces does not have the 3-space property, which corrects a theorem in an earlier paper of the authors [Studia Math. 174 (2006)]. We then solve a problem in that paper showing that $ℒ_{∞}$ spaces not containing l₁ are not necessarily ℒ-spaces.
LA - eng
KW - extension of operators; exact sequence of Banach spaces; three-space property
UR - http://eudml.org/doc/285193
ER -