A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces
Volume 211 / 2012
Studia Mathematica 211 (2012), 199-214 MSC: Primary 46B28; Secondary 46B20, 46B42, 47B10, 47L07, 47L20. DOI: 10.4064/sm211-3-2
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 $\varLambda$-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 $\mathcal W$ yielding the weak bounded approximation property?