, Volume 38, Issue 1-2, pp 58-74

Isometries between Banach spaces of Lipschitz functions

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Abstract

The Banach spaces Lip a (S, Δ), lip a (S, Δ), Lip a (S, Δ;s 0) and lip a (S, Δ;s 0) of Lipschitz functions are defined. We shall identify the extreme points of the unit balls in their corresponding dual spaces and make use of them to present a complete characterization of the isometries between these function spaces.

This paper is a part of the author’s M.Sc. thesis which was prepared under the guidance of Dr. Y. Benyamini.