The operator equation Σi=0nAn-iXBi = Y

被引：20

作者：

Bhatia, Rajendra ^{[2
]}

Uchiyama, Mitsuru ^{[1
]}

机构：

[1] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

[2] Indian Stat Inst, New Delhi 110016, India

来源：

EXPOSITIONES MATHEMATICAE | 2009年 / 27卷 / 03期

关键词：

Linear operator equation; Frechet derivative; Sylvester equation;

D O I：

10.1016/j.exmath.2009.02.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The solution of the linear operator equation: A(n-1) X + A(n-2)XB + ... + AXB(n-2) + XBn-1 = Y is given by X = ((sin pi/n)/pi) integral(infinity)(0)(t + A(n))(-1) Y(t + B-n)(-1)t(1/n) dt if the spectra of A and B are in the sector {z : z not equal 0, -pi/n < arg z < pi/n}. (C) 2009 Elsevier GmbH. All rights reserved.

引用

页码：251 / 255

页数：5

共 6 条

[1] VARIATION OF REAL POWERS OF POSITIVE OPERATORS [J].