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A note on commutativity of a linear operatorand its moore-penrose inverse

 

作者: K. G. Brock,  

 

期刊: Numerical Functional Analysis and Optimization  （Taylor Available online 1990）
卷期: Volume 11, issue 7-8  

页码: 673-678

 

ISSN:0163-0563

 

年代: 1990

 

DOI:10.1080/01630569008816396

 

出版商: Marcel Dekker, Inc.

 

数据来源: Taylor

 

摘要:

LetAbe a bounded linear operator on a Hilbert spaceH, and letA+be its Moore-Penrose inverse. A proof is given thatAandA+commute if and only ifA*=PA, wherePis an invertible bounded linear operator onH. This is an extension to infinite dimensional spaces of a result known for finite dimensionalH.

 

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