Γ-inverses of Bounded Linear Operators  

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

机构地区：[1]School of Science,Shanghai Institute of Technology [2]College of Mathematics and Information Science,Shaanxi Normal University [3]Department of Mathematics,Tongji University

出　　处：《Acta Mathematica Sinica,English Series》2014年第4期675-680,共6页数学学报（英文版）

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)

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）.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）.

关 键 词：Generalized inverse F-inverse Moore-Penrose inverse 

分 类 号：O177[理学—数学] O177.1[理学—基础数学]