We consider some stability aspects of the classical problem of extension of C(K)-valued operators. We introduce the class ℒ of Banach spaces of Lindenstrauss-Pełczyński type as those such that every operator from a subspace of c₀ into them can be extended to c₀. We show that all ℒ-spaces are of type but not conversely. Moreover, -spaces will be characterized as those spaces E such that E-valued operators from w*(l₁,c₀)-closed subspaces of l₁ extend to l₁. Regarding examples we will show that every separable -space is a quotient of two ℒ-spaces; also, -spaces not containing c₀ are ℒ-spaces; the complemented subspaces of C(K) and the separably injective spaces are subclasses of the ℒ-spaces and we show that the former does not contain the latter. Regarding stability properties, we prove that quotients of an ℒ-space by a separably injective space and twisted sums of ℒ-spaces are ℒ-spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-1,
author = {Jes\'us M. F. Castillo and Yolanda Moreno and Jes\'us Su\'arez},
title = {On Lindenstrauss-Pe\l czy\'nski spaces},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {213-231},
zbl = {1104.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-1}
}
Jesús M. F. Castillo; Yolanda Moreno; Jesús Suárez. On Lindenstrauss-Pełczyński spaces. Studia Mathematica, Tome 173 (2006) pp. 213-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-1/