A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces
Studia Mathematica (2012)
- Volume: 211, Issue: 3, page 199-214
- ISSN: 0039-3223
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topAleksei 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 -
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