2-Local isometries between spaces of functions of bounded variation
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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.
KeywordsLinear isometry 2-Local isometry Functions of bounded variation Absolutely continuous functions
Mathematics Subject ClassificationPrimary 47B38 Secondary 46J10 47B33
- 6.Hatori, O., Oi, S.: 2-local isometries on function spaces. Contemp. Math. 737, 89–106 (2019)Google Scholar