Linear isometries on subalgebras of uniformly continuous functions

Abstract

We describe the linear surjective isometries between various subalgebras of uniformly continuous bounded functions defined on closed subsets of Banach spaces.

Biseparating maps between Lipschitz function spaces

“…This proves the lemma. 2The next lemma is a Lipschitz version (with a similar proof) of the result given in[6, Lemma 3.4] in the context of uniformly continuous functions.…”