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）.
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)
