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| Γ-inverses of Bounded Linear Operators | |
| 基金项目： | 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(H) be the algebra of all the bounded linear operators on a Hilbert space H.For A,P and Q in B(H),if there exists an operator X∈ B(H) such thatAP X QA=A,X QAP X=X,(QAP X)*=QAP X and(X QAP)*=X QAP,then X is said to be the Γ-inverse of A associated with P and Q,and denoted by AP,Q+.In this note,we present some necessary and su?cient conditions for which A+P,Qexists,and give an explicit representation of AP,Q+(if AP,Q+exists). |
| 关 键 词： | 界线性算子 希尔伯特空间 充分必要条件 算子代数 有界 |
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