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

TL;DR

This paper characterizes 2-local standard isometries on vector-valued Lipschitz function spaces, showing they can be described via generalized composition operators and exploring conditions for their linearity and surjectivity.

Contribution

It provides a description of 2-local isometries on vector-valued Lipschitz spaces in terms of generalized composition operators and analyzes their linearity and surjectivity.

Findings

2-local isometries can be characterized by generalized composition operators

Conditions are identified under which 2-local isometries are linear and surjective

The work extends understanding of isometries in vector-valued Lipschitz function spaces

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.