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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 $\varLambda$-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?