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WEIGHTED CORE–EP INVERSE AND WEIGHTED CORE–EP PRE-ORDERS IN A $C^{\ast }$-ALGEBRA
Published online by Cambridge University Press: 18 October 2019
Abstract
We define extensions of the weighted core–EP inverse and weighted core–EP pre-orders of bounded linear operators on Hilbert spaces to elements of a $C^{\ast }$-algebra. Some properties of the weighted core–EP inverse and weighted core–EP pre-orders are generalized and some new ones are proved. Using the weighted element, the weighted core–EP pre-order, the minus partial order and the star partial order of certain elements, new weighted pre-orders are presented on the set of all $wg$-Drazin invertible elements of a $C^{\ast }$-algebra. Applying these results, we introduce and characterize new partial orders which extend the core–EP pre-order to a partial order.
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- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by L. O. Clark
The author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, grant no. 174007.
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