On Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, and Jesús Suárez. "On Lindenstrauss-Pełczyński spaces." Studia Mathematica 174.3 (2006): 213-231. <http://eudml.org/doc/285127>.

@article{JesúsM2006,
abstract = {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 $ℒ_\{∞\}$ but not conversely. Moreover, $ℒ_\{∞\}$-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 $ℒ_\{∞\}$-space is a quotient of two ℒ-spaces; also, $ℒ_\{∞\}$-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.},
author = {Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez},
journal = {Studia Mathematica},
keywords = {extension of operators; exact sequence of Banach spaces; three-space property; operator ideal},
language = {eng},
number = {3},
pages = {213-231},
title = {On Lindenstrauss-Pełczyński spaces},
url = {http://eudml.org/doc/285127},
volume = {174},
year = {2006},
}

TY - JOUR
AU - Jesús M. F. Castillo
AU - Yolanda Moreno
AU - Jesús Suárez
TI - On Lindenstrauss-Pełczyński spaces
JO - Studia Mathematica
PY - 2006
VL - 174
IS - 3
SP - 213
EP - 231
AB - 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 $ℒ_{∞}$ but not conversely. Moreover, $ℒ_{∞}$-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 $ℒ_{∞}$-space is a quotient of two ℒ-spaces; also, $ℒ_{∞}$-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.
LA - eng
KW - extension of operators; exact sequence of Banach spaces; three-space property; operator ideal
UR - http://eudml.org/doc/285127
ER -