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Positivity

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2-Local isometries between spaces of functions of bounded variation

  • Maliheh HosseiniEmail author
Article
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Abstract

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.

Keywords

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

Mathematics Subject Classification

Primary 47B38 Secondary 46J10 47B33 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of MathematicsK. N. Toosi University of TechnologyTehranIran

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