Two-sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice

被引：0
|
作者：
Gil, Michael [1 ]
机构：
[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
来源：
MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 8-9期
关键词：
Operator equation; positivity of solutions; functions of non-commuting operators; MATRIX-VALUED FUNCTIONS; SPECTRUM;
D O I：
10.1002/mana.201300252
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A and (A) over tilde be bounded linear operators in a Banach lattice B, and M be a positive operator in B. The paper deals with the equation Sigma(m1)(j=0)Sigma(m2)(k=0)c(jk) A(j) X (A) over tilde (k) = M, where X should be found and c(jk) are real numbers. Two-sided estimates and positivity conditions for a solution of that equation are established. The illustrative examples are also presented. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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页码：974 / 981
页数：8
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