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The reverse order law for {1,2,3}-inverse of a two-operator product
Haiyan Zhang,Ji Guoxing
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062
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Funding: the National Natural Science Foundation of China（No.No.10971123）, the Specialized Research Fund for the Doctoral Program of Higher Education（No.No.20090202110001）
Opened online: 9 March 2012
Accepted by: none
Citation: Haiyan Zhang,Ji Guoxing.The reverse order law for {1,2,3}-inverse of a two-operator product[OL]. [ 9 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4469607
 
 
The reverse order law for {1,2,3}-inverse of a two-operator product is mainly investigated by making full use of block-operator matrix technique in this paper. The necessary and sufficient conditions for AB{1,2,3} includes B{1,2,3}A{1,2,3} and AB{1,2,4} includes B{1,2,4}A{1,2,4} are presented when all ranges R(A), R(B) and R(AB) are closed.
Keywords:Linear operator; Block-operator matrix; Generalized inverse; Reverse order law
 
 
 

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