DECOMPOSITION IN DIRECT SUM OF SEMINORMED VECTOR SPACES AND MAZUR-ULAM THEOREM

被引：0

作者：

Dovgoshey, Oleksiy ^{[1
,2
]}

Prestin, Juergen ^{[3
]}

Shevchuk, Igor ^{[4
]}

机构：

[1] Inst Appl Math & Mech NASU, Dept Theory Funct, UA-84100 Slovyansk, Ukraine

[2] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

[3] Univ Lubeck, Inst Math, D-23562 Lubeck, Germany

[4] Tars Shevchenko Natl Univ Kyiv, Fac Mech & Math, UA-01601 Kyiv, Ukraine

来源：

MATHEMATICA SLOVACA | 2024年 / 74卷 / 01期

关键词：

Seminormed vector space; isometric embedding; direct sum; Mazur-Ulam theorem;

D O I：

10.1515/ms-2024-0010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur-Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear. (c) 2024 Mathematical Institute Slovak Academy of Sciences

引用

页码：143 / 150

页数：8

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