Displaying similar documents to “The l 1 n problem and degrees of non-reflexivity”

Local dual spaces of a Banach space

Manuel González, Antonio Martínez-Abejón (2001)

Studia Mathematica

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We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing...

What is "local theory of Banach spaces"?

Albrecht Pietsch (1999)

Studia Mathematica

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Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.