Isometries between completely regular vector-valued function spaces

2020/03/02 by Mojahedi, Mojtaba, Sady, Fereshteh
#46J10 #47B33 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2003.01566

Abstract

In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces A and B of C₀(X,E) and C₀(Y,F) where X and Y are locally compact Hausdorff spaces and E and F are normed spaces, not assumed to be neither strictly convex nor complete. We show that for a class of normed spaces F satisfying a new defined property related to their T-sets, such an isometry is a (generalized) weighted composition operator up to a translation. Then we apply the result to study surjective isometries between A and B whenever A and B are equipped with certain norms rather than the supremum norm. Our results unify and generalize some recent results in this context.

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