Characterization of inner product spaces by means of orthogonally additive mappings

被引：0

作者：

Rätz J. ^{[1
]}

机构：

[1] Mathematisches Institut, Universität Bern, CH-3012 Bern

来源：

Aequationes mathematicae | 1999年 / 58卷 / 1-2期

关键词：

Uniqueness Property; Normed Space; Additive Mapping; Product Space; Orthogonality Relation;

D O I：

10.1007/s000100050012

中图分类号：

学科分类号：

摘要：

There are cases in which characterizations of inner product spaces among normed spaces underlie a dimension condition. E.g., symmetry of the Blaschke-Birkhoff- James orthogonality as well as a certain uniqueness property of the Diminnie orthogonality work only for dimension at least three but do collapse for dimension two. It is the aim of this paper to exhibit some of the contrasts between dimensions 2 and 3, specifically to show that if orthogonally additive mappings instead of the orthogonality relation itself are used, the two-dimensional case is no longer exceptional. This makes the characterization situation more satisfactory. Our emphasis is on the Diminnie orthogonality. © Birkhäuser Verlag, Basel, 1999.

引用

页码：111 / 117

页数：6

共 18 条

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