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2-Local uniform isometries between complex Lipschitz algebras

  • Davood AlimohammadiEmail author
  • Reyhaneh Bagheri
Original Paper

Abstract

Let (Xd) be a metric space and let \(\mathrm{Lip}(X,d) \) denote the complex algebra of all complex-valued bounded functions f on X for which f is a Lipschitz function on \(\mathrm{(X,d)}\). In this paper we give a complete description of all 2-local real and complex uniform isometries between \(\mathrm{Lip}(X,d) \) and \(\mathrm{Lip(Y},\rho \mathrm{)}\), where (Xd) and \((Y,\rho )\) are compact metric spaces. In particular, we show that every 2-local real (complex, respectively) uniform isometry from \(\mathrm{Lip}(X,d) \) to \(\mathrm{Lip(Y,}\rho \mathrm{)}\) is a surjective real (complex, respectively) linear uniform isometry.

Keywords

Banach algebra 2-local isometry Linear isometry Lipschitz homeomorphism 

Mathematics Subject Classification

47B38 46J10 

Notes

Acknowledgements

The authors would like to thank the referee for his/her valuable comments and suggestions.

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceArak UniversityArakIran

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