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

作者：Lissitsin Aleksei^*

来源：Studia Mathematica, 2012, 211(3): 199-214.

DOI：10.4064/sm211-3-2

• Banach spaces
• Banach lattices
• convex
• strong and weak bounded approximation properties
• factorization of operators
• operator ideals

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 Lambda-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?

• 出版日期2012