论向量值小李普希茨函数的巴拿赫空间的第二对偶空间

Pub Date : 2020-09-21 DOI:10.2206/kyushujm.75.235

Shinnosuke Izumi

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引用次数: 1

摘要

设\(X\)是紧度量空间\(E\)是巴拿赫空间。\(\lip (X, E)\)表示\(X\)上所有\(E\)值小Lipschitz函数的Banach空间。在若干条件下，我们证明\(\lip (X, E)^{**}\)与\(E^{**}\) -值Lipschitz函数\(\Lip(X, E^{**})\)的Banach空间是等距同构的。此外，我们描述了从\(\lip (X, E)^{**}\)到\(\Lip (X, E^{**})\)的等距同构。

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ON THE SECOND DUAL SPACE OF THE BANACH SPACE OF VECTOR-VALUED LITTLE LIPSCHITZ FUNCTIONS

Let \(X\) be a compact metric space and \(E\) be a Banach space. \(\lip (X, E)\) denotes the Banach space of all \(E\)-valued little Lipschitz functions on \(X\). We show that \(\lip (X, E)^{**}\) is isometrically isomorphic to Banach space of \(E^{**}\)-valued Lipschitz functions \(\Lip(X, E^{**})\) under several conditions. Moreover, we describe the isometric isomorphism from \(\lip (X, E)^{**}\) to \(\Lip (X, E^{**})\).

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