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

Shinnosuke Izumi

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

Functional Analysis 2020-09-22 v1

Authors: Shinnosuke Izumi

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 $\Lip (X, E^{**})$ .

Keywords

banach space little lipschitz functions vector-valued second dual isometric isomorphism compact metric space

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@article{arxiv.2009.09721,
  title  = {On the second dual space of Banach space of vector-valued little Lipschitz functions},
  author = {Shinnosuke Izumi},
  journal= {arXiv preprint arXiv:2009.09721},
  year   = {2020}
}

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13 pages

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

Abstract

Keywords

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