2-Local isometries between spaces of functions of bounded variation


Given two subsets X and Y of the real line with at least two points, we apply results on surjective linear isometries between Banach spaces of all functions of bounded variation BV(X) and BV(Y) to show that every 2-local isometry \(T:BV(X)\longrightarrow BV(Y)\) is a constant multiple of an isometric linear algebra isomorphism. Moreover, similar results are given for the closed subspaces of BV(X) and BV(Y) consisting of all continuous (resp. absolutely continuous) functions when X and Y are compact.

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Correspondence to Maliheh Hosseini.

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Hosseini, M. 2-Local isometries between spaces of functions of bounded variation. Positivity 24, 1101–1109 (2020). https://doi.org/10.1007/s11117-019-00721-0

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  • Linear isometry
  • 2-Local isometry
  • Functions of bounded variation
  • Absolutely continuous functions

Mathematics Subject Classification

  • Primary 47B38
  • Secondary 46J10
  • 47B33