Γ-inverses of Bounded Linear Operators

作     者：Xiao Ming XU Hong Ke DU Xiao Chun FANG 

作者机构：School of ScienceShanghai Institute of Technology College of Mathematics and Information ScienceShaanxi Normal University Department of MathematicsTongji University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第4期

页      面：675-680页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Research Foundation of Shanghai Institute of Technology for Talented Scholars(Grant No.1020K126021-YJ2012-21) Special Foundation for Excellent Young College and University Teachers(Grant No.405ZK12YQ21-ZZyyy12021) supported by National Natural Science Foundation of China(Grant No.11171197) supported by National Natural Science Foundation of China(Grant No.11071188) 

主　　题：Generalized inverse F-inverse Moore-Penrose inverse 

摘      要：Let B（Н） be the algebra of all the bounded linear operators on a Hilbert space Н. For A, P and Q in B（Н）, if there exists an operator X ∈ B（Н） such that APXQA = A, XQAPX = X, （QAPX）^＊ = QAPX and （XQAP）^＊ = XQAP, then X is said to be the F-inverse of A associated with P and Q, and denoted by A^＋P,Q. In this note, we present some necessary and sufficient conditions for which A^＋P,Q exists, and give an explicit representation of A^＋PQ （if A^＋P,Q exists）.