Generalizations of Alesandrov problem and Mazur-Ulam theorem for two-isometries and two-expansive mappings
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 771-782
https://doi.org/10.4134/CKMS.c180200
Published online July 31, 2019
Hamid Khodaei, Abdulqader Mohammadi
Malayer University; Malayer University
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.
Keywords : Alesandrov problem, $C^*$-algebra, Mazur-Ulam theorem, strictly convex, two-isometry, two-expansive mapping
MSC numbers : 46B04, 47A62, 47B99, 52A07
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