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

2017/08/09 by Jiménez-Vargas, Antonio, Li, Lei, Peralta, Antonio M. +2
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1708.02897

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 \hboxLip(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 \hboxLip(X,E) is both linear and surjective.

Related

• Noncompactness and noncompleteness in isometries of Lipschitz spaces
• 2-local isometries on function spaces
• Isometric composition operators on Lipschitz spaces
• Weighted composition operators preserving various Lipschitz constants
• Some results on isometric composition operators on Lipschitz spaces