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Local duality for Banach spaces. (English) Zbl 1330.46017

Summary: A local dual of a Banach space \(X\) is a subspace of the dual \(X^\ast\) which can replace the whole dual space when dealing with finite dimensional subspaces. This notion arose as a development of the principle of local reflexivity, and it is very useful when a description of \(X^\ast\) is not available.{ }We give an exposition of the theory of local duality for Banach spaces, including the main properties, examples and applications, and comparing the notion of local dual with some other weaker properties of the subspaces of the dual of a Banach space.

MSC:

46B07 Local theory of Banach spaces
46B08 Ultraproduct techniques in Banach space theory
46B10 Duality and reflexivity in normed linear and Banach spaces
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