Displaying similar documents to “A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces”

On bounded approximation properties of Banach spaces

Eve Oja (2010)

Banach Center Publications

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This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?

The impact of the Radon-Nikodym property on the weak bounded approximation property.

Eve Oja (2006)

RACSAM

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A Banach space X is said to have the weak λ-bounded approximation property if for every separable reflexive Banach space Y and for every compact operator T : X → Y, there exists a net (Sα) of finite-rank operators on X such that supα ||TSα|| ≤ λ||T|| and Sα → IX uniformly on compact subsets of X. We prove the following theorem. Let X** or Y* have the Radon-Nikodym property;...

Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of c 0 , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...

Property (wM*) and the unconditional metric compact approximation property

Ăsvald Lima (1995)

Studia Mathematica

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The main objective of this paper is to give a simple proof for a larger class of spaces of the following theorem of Kalton and Werner. (a) X has property (M*), and (b) X has the metric compact approximation property Our main tool is a new property (wM*) which we show to be closely related to the unconditional metric approximation property.