On partial orders of Hilbert space operators

Author： Jose Shani   Sivakumar K.C.  

Publisher： Taylor & Francis Ltd

E-ISSN： 1563-5139|63|7|1423-1441

ISSN： 0308-1087

Source： Linear and Multilinear Algebra, Vol.63, Iss.7, 2015-07, pp. : 1423-1441

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Abstract

First, an overview of partial orders defined on bounded linear operators on an infinite-dimensional Hilbert space is presented. A definition for the core inverse of operators on a Hilbert space is proposed. Extensions of the sharp and the core partial orders are considered. An explicit formula for the core inverse of matrices is obtained using a full-rank factorization. Relationships between all these partial orders and formula for generalized inverses of differences of operators, when they are related with respect to these partial orders, are investigated.

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