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2-local standard isometries on vector-valued Lipschitz function spaces. (English) Zbl 06852159

Summary: 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 \(\operatorname{Lip}(X, E)\) 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 \(\operatorname{Lip}(X, E)\) is both linear and surjective.

MSC:

47-XX Operator theory
54-XX General topology
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