Resumen de Bounded approximation properties in terms of C[0, 1]

Asvald Lima, Vegard Lima, Eve Oja

• Let X be a Banach space and let I be the Banach operator ideal of integral operators. We prove that X has the λ-bounded approximation property (λ-BAP) if and only if for every operator T∈I(X,C[0,1]∗) there exists a net (Sα) of finite-rank operators on X such that Sα→IX pointwise and 26767 \limsup_\alpha\|TS_\alpha\|_{\mathcal I}\leq\lambda\|T\|_{\mathcal I}. 26767 We also prove that replacing I by the ideal N of nuclear operators yields a condition which is equivalent to the weak λ-BAP.