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1 Studia Mathematica

1 2012

1 Lissitsin A.

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

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Lissitsin A.

2012

tom 211

nr 3

199-214

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?