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arXiv · 2009.09721

On the second dual space of Banach space of vector-valued little Lipschitz functions

Shinnosuke Izumi
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Abstract

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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Shinnosuke Izumi. 2020-09-21. On the second dual space of Banach space of vector-valued little Lipschitz functions. https://arxiv.org/abs/2009.09721

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