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 spaces not containing l₁ are not necessarily ℒ-spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-1,
author = {Jes\'us M. F. Castillo and Yolanda Moreno and Jes\'us Su\'arez},
title = {The structure of Lindenstrauss-Pe\l czy\'nski spaces},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {105-115},
zbl = {1192.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-1}
}
Jesús M. F. Castillo; Yolanda Moreno; Jesús Suárez. The structure of Lindenstrauss-Pełczyński spaces. Studia Mathematica, Tome 192 (2009) pp. 105-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-1/