Generalizations of Alesandrov problem and Mazur-Ulam theorem for two-isometries and two-expansive mappings
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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.
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.
참고문헌 (14)
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