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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.
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참고문헌 (14)
참고문헌 신청
Jim Agler / 1995 / m-Isometric transformations of Hilbert space, I / Integral Equations and Operator Theory 21(4):383~429
A. D. Aleksandrov / 1970 / Mappings of families of sets / Dokl. Akad. Nauk SSSR 191:503~506
J. A. Baker / 1971 / Isometries in Normed Spaces / The American Mathematical Monthly 78(6):655
Frédéric Bayart / 2011 / m-isometries on Banach spaces / Mathematische Nachrichten 284(17-18):2141~2147
Hahng-Yun Chu / 2007 / On the Mazur–Ulam problem in linear 2-normed spaces / Journal of Mathematical Analysis and Applications 327(2):1041~1045
A. D. Aleksandrov / 1970 / Mappings of families of sets / Dokl. Akad. Nauk SSSR 191:503~506
J. A. Baker / 1971 / Isometries in Normed Spaces / The American Mathematical Monthly 78(6):655
Frédéric Bayart / 2011 / m-isometries on Banach spaces / Mathematische Nachrichten 284(17-18):2141~2147
Hahng-Yun Chu / 2007 / On the Mazur–Ulam problem in linear 2-normed spaces / Journal of Mathematical Analysis and Applications 327(2):1041~1045
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