Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZATIONS OF ALESANDROV PROBLEM AND MAZUR-ULAM THEOREM FOR TWO-ISOMETRIES AND TWO-EXPANSIVE MAPPINGS

  • Khodaei, Hamid (Faculty of Mathematical Sciences and Statistics Malayer University) ;
  • Mohammadi, Abdulqader (Faculty of Mathematical Sciences and Statistics Malayer University)
  • Received : 2018.05.08
  • Accepted : 2019.04.09
  • Published : 2019.07.31
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Abstract

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.

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References

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