Bounded approximation properties in terms of C[0,1] - Lima, Åsvald; Lima, Vegard; Oja, Eve (Mathematica Scandinavica, 2012)
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 TI(X,C[0,1]^*) there exists a net (S_α) of finite-rank operators on X such that S_α→ I_X pointwise and 26767 _α\|TS_α\|_I≤λ\|T\|_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.