Generalized gyrovector spaces and a Mazur-Ulam theorem

被引：21

作者：

Abe, Toshikazu ^{[1
]}

Hatori, Osamu ^{[2
]}

机构：

[1] Niigata Univ, Fac Engn, Dept Informat Engn, Niigata 95021, Japan

[2] Niigata Univ, Fac Sci, Dept Math, Niigata 95021, Japan

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2015年 / 87卷 / 3-4期

关键词：

gyrovector spaces; a Mazur-Ulam theorem; ISOMETRIES; MATRICES; ELEMENTS; MAPS;

D O I：

10.5486/PMD.2015.7234

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we introduce the notion of a generalized gyrovector space. The set of all positive invertible elements in a unital C*-algebra is an example. We study surjective gyrometric preserving maps and show that such maps also preserve the algerbraic structures. As an application we exhibit a structure theorem for maps which preserve the metric of Thompson's type.

引用

页码：393 / 413

页数：21

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