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arXiv · 2106.11546

Isometries and hermitian operators on spaces of vector-valued Lipschitz maps

Shiho Oi
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Abstract

We study hermitian operators and isometries on spaces of vector-valued Lipschitz maps with the sum norm: $\|\cdot\|_{\infty}+L(\cdot)$. There are two main theorems in this paper. Firstly, we prove that every hermitian operator on $\operatorname{Lip}(X,E)$, where $E$ is a complex Banach space, is a generalized composition operator. Secondly, we give a complete description of unital surjective complex linear isometries on $\operatorname{Lip}(X,\mathcal{A})$ where $\mathcal{A}$ is a unital factor $C^{*}$-algebra. These results improve previous results stated by the author.

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Shiho Oi. 2021-06-22. Isometries and hermitian operators on spaces of vector-valued Lipschitz maps. https://doi.org/10.1017/s1474748023000415

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