Some duality results on bounded approximation properties of pairs

Eve Oja; Silja Treialt

Eve Oja ; Silja Treialt

Studia Mathematica, Tome 215 (2013), p. 79-94 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $S_{α} (Y) \subset Y$ and $| | S_{α} | | \leq λ$ 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.

Publié le : 2013-01-01

Zbl 1293.46012

EUDML-ID : urn:eudml:doc:286415

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Eve Oja; Silja Treialt. Some duality results on bounded approximation properties of pairs. Studia Mathematica, Tome 215 (2013) pp. 79-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-5/