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Isometries between completely regular vector-valued function spaces

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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Correspondence to Fereshteh Sady.

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Mojahedi, M., Sady, F. Isometries between completely regular vector-valued function spaces. Period Math Hung 84, 361–370 (2022). https://doi.org/10.1007/s10998-021-00413-x

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  • DOI: https://doi.org/10.1007/s10998-021-00413-x

Keywords

  • Real-linear isometries
  • Vector-valued function spaces
  • T-sets
  • Strictly convex

Mathematics Subject Classification

  • Primary 47B38
  • 47B33
  • Secondary 46J10