1 results
WEIGHTED CORE–EP INVERSE AND WEIGHTED CORE–EP PRE-ORDERS IN A
$C^{\ast }$-ALGEBRA
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 111 / Issue 1 / August 2021
- Published online by Cambridge University Press:
- 18 October 2019, pp. 76-110
- Print publication:
- August 2021
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- Article
- Export citation
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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.
