A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces

Aleksei Lissitsin. "A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces." Studia Mathematica 211.3 (2012): 199-214. <http://eudml.org/doc/285874>.

@article{AlekseiLissitsin2012,
abstract = {We consider convex versions of the strong approximation property and the weak bounded approximation property and develop a unified approach to their treatment introducing the inner and outer Λ-bounded approximation properties for a pair consisting of an operator ideal and a space ideal. We characterize this type of properties in a general setting and, using the isometric DFJP-factorization of operator ideals, provide a range of examples for this characterization, eventually answering a question due to Lima, Lima, and Oja: Are there larger Banach operator ideals than 𝒲 yielding the weak bounded approximation property?},
author = {Aleksei Lissitsin},
journal = {Studia Mathematica},
keywords = {Banach spaces; Banach lattices; strong and weak bounded approximation properties; factorization of operators; operator ideals},
language = {eng},
number = {3},
pages = {199-214},
title = {A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces},
url = {http://eudml.org/doc/285874},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Aleksei Lissitsin
TI - A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 3
SP - 199
EP - 214
AB - We consider convex versions of the strong approximation property and the weak bounded approximation property and develop a unified approach to their treatment introducing the inner and outer Λ-bounded approximation properties for a pair consisting of an operator ideal and a space ideal. We characterize this type of properties in a general setting and, using the isometric DFJP-factorization of operator ideals, provide a range of examples for this characterization, eventually answering a question due to Lima, Lima, and Oja: Are there larger Banach operator ideals than 𝒲 yielding the weak bounded approximation property?
LA - eng
KW - Banach spaces; Banach lattices; strong and weak bounded approximation properties; factorization of operators; operator ideals
UR - http://eudml.org/doc/285874
ER -