Sobczyk's theorem and the Bounded Approximation Property

Jesús M. F. Castillo, and Yolanda Moreno. "Sobczyk's theorem and the Bounded Approximation Property." Studia Mathematica 201.1 (2010): 1-19. <http://eudml.org/doc/285824>.

@article{JesúsM2010,
abstract = {Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.},
author = {Jesús M. F. Castillo, Yolanda Moreno},
journal = {Studia Mathematica},
keywords = {extension and lifting of operators; separable injectivity; bounded approximation property; twisted sums of Banach spaces},
language = {eng},
number = {1},
pages = {1-19},
title = {Sobczyk's theorem and the Bounded Approximation Property},
url = {http://eudml.org/doc/285824},
volume = {201},
year = {2010},
}

TY - JOUR
AU - Jesús M. F. Castillo
AU - Yolanda Moreno
TI - Sobczyk's theorem and the Bounded Approximation Property
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 1
SP - 1
EP - 19
AB - Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.
LA - eng
KW - extension and lifting of operators; separable injectivity; bounded approximation property; twisted sums of Banach spaces
UR - http://eudml.org/doc/285824
ER -