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Isometry on Linear $n$-G-quasi Normed Spaces

  Published:2016-11-03
 Printed: Jun 2017
  • Yumei Ma,
    Department of Mathematics, Dalian Nationalities University, 116600 Dalian, China
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Abstract

This paper generalizes the Aleksandrov problem: the Mazur-Ulam theorem on $n$-G-quasi normed spaces. It proves that a one-$n$-distance preserving mapping is an $n$-isometry if and only if it has the zero-$n$-G-quasi preserving property, and two kinds of $n$-isometries on $n$-G-quasi normed space are equivalent; we generalize the Benz theorem to n-normed spaces with no restrictions on the dimension of spaces.
Keywords: $n$-G-quasi norm, Mazur-Ulam theorem, Aleksandrov problem, $n$-isometry, $n$-0-distance $n$-G-quasi norm, Mazur-Ulam theorem, Aleksandrov problem, $n$-isometry, $n$-0-distance
MSC Classifications: 46B20, 46B04, 51K05 show english descriptions Geometry and structure of normed linear spaces
Isometric theory of Banach spaces
General theory
46B20 - Geometry and structure of normed linear spaces
46B04 - Isometric theory of Banach spaces
51K05 - General theory
 

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