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arXiv · 1708.02897

2-local standard isometries on vector-valued Lipschitz function spaces

Antonio Jiménez-Vargas·Lei Li·Antonio M. Peralta·Liguang Wang·Ya-Shu Wang
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Abstract

Under the right conditions on a compact metric space $X$ and on a Banach space $E$, we give a description of the $2$-local (standard) isometries on the Banach space $\hbox{Lip}(X,E)$ of vector-valued Lipschitz functions from $X$ to $E$ in terms of a generalized composition operator, and we study when every $2$-local (standard) isometry on $\hbox{Lip}(X,E)$ is both linear and surjective.

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Antonio Jiménez-Vargas, Lei Li, Antonio M. Peralta, Liguang Wang, Ya-Shu Wang. 2017-08-09. 2-local standard isometries on vector-valued Lipschitz function spaces. https://arxiv.org/abs/1708.02897

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