Some duality results on bounded approximation properties of pairs
Tom 217 / 2013
Studia Mathematica 217 (2013), 79-94
MSC: Primary 46B28; Secondary 46B20, 46B10, 47B10.
DOI: 10.4064/sm217-1-5
Streszczenie
The main result is as follows. Let be a Banach space and let Y be a closed subspace of X. Assume that the pair (X^{*}, Y^{\perp }) has the \lambda -bounded approximation property. Then there exists a net ( S_\alpha ) of finite-rank operators on X such that S_\alpha (Y) \subset Y and \| S_\alpha \| \leq \lambda for all \alpha , and ( S_\alpha ) and ( S^{*}_\alpha ) converge pointwise to the identity operators on X and X^{*}, respectively. This means that the pair (X,Y) has the \lambda -bounded duality approximation property.
