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Some duality results on bounded approximation properties of pairs

Eve Oja, Silja Treialt (2013)

Studia Mathematica

The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair ( X * , Y ) has the λ-bounded approximation property. Then there exists a net ( S α ) of finite-rank operators on X such that S α ( Y ) Y and | | S α | | λ for all α, and ( S α ) and ( S * α ) converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.

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