A STRONG VERSION OF THE BIRKHOFF-JAMES ORTHOGONALITY IN HILBERT C*-MODULES

被引：35
|
作者：
Arambasic, Ljiljana [1 ]
Rajic, Rajna [2 ]
机构：
[1] Univ Zagreb, Dept Math, Zagreb 10000, Croatia
[2] Univ Zagreb, Fac Min Geol & Petr Engn, Zagreb 10000, Croatia
来源：
ANNALS OF FUNCTIONAL ANALYSIS | 2014年 / 5卷 / 01期
关键词：
Birkhoff-James orthogonality; state; Hilbert C*-module; C*-algebra; VALUED TRIANGLE EQUALITY; PRESERVING MAPPINGS;
D O I：
10.15352/afa/1391614575
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we introduce a strong version of the Birkhoff-James orthogonality in Hilbert C*-modules. More precisely, we consider elements x and y of a Hilbert C*-module V over a C*-algebra A which satisfy parallel to x parallel to <= parallel to x + ya parallel to for all a is an element of A. We show that this relation can be described as the Birkhoff-James orthogonality of appropriate elements of V, and characterized in terms of states acting on the underlying C*-algebra A. Some analogous relations of this type are considered as well.
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页码：109 / 120
页数：12
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