A characterization of Hilbert C*-modules over commutative C*-algebras

被引：0
作者：
Akrami, Rasoul [1 ]
Janfada, Ali Reza [1 ]
Miri, Mohammad Reza [1 ]
机构：
[1] Univ Birjand, Fac Math & Stat, Dept Math, POB 414, Birjand 9717851367, Iran
来源：
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA | 2018年 / 11卷 / 04期
关键词：
Commutative C*-algebras; Hilbert C*-modules; Irreducible representation;
D O I：
10.1007/s40574-017-0152-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M be a Hilbert C*-module. Set vertical bar x vertical bar = < x, x >(1/2) for every x. M and C = {< x, y >: x, y is an element of M}. We prove that vertical bar xa vertical bar = vertical bar x vertical bar vertical bar a vertical bar for every x is an element of M and a is an element of C if and only if C is a commutative C*-algebra.
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页码：557 / 561
页数：5
相关论文
共 6 条
[1]   On the C*-valued triangle equality and inequality in Hilbert C*-modules [J].
Arambasic, Lj. ;
Rajic, R. .
ACTA MATHEMATICA HUNGARICA, 2008, 119 (04) :373-380
[2]  
Harte R., 2006, FILOMAT, V20, P51
[3]   A NOTE ON THE TRIANGLE INEQUALITY FOR THE C*-VALUED NORM ON A HILBERT C*-MODULE [J].
Jiang, Runliang .
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2013, 16 (03) :743-749
[4]  
Kolarec B, 2009, MATH INEQUAL APPL, V12, P745
[5]  
Lance E. C., 1995, LONDON MATH SOC LECT, V210
[6]  
Murphy G. J., 1990, C ALGEBRAS OPERATOR
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