Some duality results on bounded approximation properties of pairs

• Autorzy: Eve Oja , Silja Treialt
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B10: Duality and reflexivity
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 217
• Numer: 1
• Strony: 79-94

Daty

wydano

2013

Twórcy

autor

Eve Oja

• Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, 50409 Tartu, Estonia
• Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn, Estonia

autor

Silja Treialt

• Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, 50409 Tartu, Estonia

Identyfikatory

DOI

10.4064/sm217-1-5