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Some duality results on bounded approximation properties of pairs

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Oja E., Treialt S.

Studia Mathematica

2013

tom 217

nr 1

79-94

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.

Ograniczanie wyników

1 Studia Mathematica

1 Oja E.

1 Treialt S.

1 2013

Wyniki wyszukiwania

Some duality results on bounded approximation properties of pairs