Positive and real-positive solutions to the equation axa* = c in C*-algebras

被引：36

作者：

Cvetkovic-Ilic, D.

Dajic, Alegra

Koliha, J. J.

机构：

[1] Univ Nis, Fac Math & Sci, Nish 18000, Serbia

[2] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia

来源：

LINEAR & MULTILINEAR ALGEBRA | 2007年 / 55卷 / 06期

关键词：

C*-algebra; regular element; Moore-Penrose inverse; equation in a C*-algebra; positive solution; real-positive solution; Hilbert space; operator equation; matrix equation;

D O I：

10.1080/03081080701248112

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain new representations for the general positive and real-positive solutions of the equation axa* = c in a C*- algebra using the characterization of positivity based on a matrix representation of an element and the generalized Schur complement. Applications to the equation AXA* = C for operators between Hilbert spaces and for finite matrices are given.

引用

页码：535 / 543

页数：9

共 13 条

[1] CONDITIONS FOR POSITIVE AND NONNEGATIVE DEFINITENESS IN TERMS OF PSEUDOINVERSES [J].