Abstract
In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces A and B of $$C_0(X,E)$$ and $$C_0(Y,F)$$ where X and Y are locally compact Hausdorff spaces and E and F are normed spaces, not assumed to be either strictly convex or complete. We show that for a class of normed spaces F satisfying a newly 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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