Splitting of Operators and Operator Equations

被引：0
|
作者：
Deng, Chun Yuan [1 ]
Zhang, Wan Yu [1 ]
机构：
[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2023年 / 39卷 / 06期
关键词：
Projection; positive operator; operator equation; Moore-Penrose inverse; POSITIVE SOLUTIONS; RANGE INCLUSION; PRODUCTS; AX; PROJECTIONS; INVERSES; XB;
D O I：
10.1007/s10114-023-1439-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the splitting operators into the product of two positive operators. For given operators A and T E t3(7-1) with A = 0 and R(A) = R(T), if T can be splitted as T = AX for some positive operator X, then the existence of X and the properties of T are studied. The related research are the solutions of operator equations T = XAX and TX = XAX, which have some particular properties and broad applications in many fields. The conditions for the existence of solutions or idempotent solutions of these kinds of equations are studied and new representations of the general solutions are given.
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页码：1085 / 1100
页数：16
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