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Algebra |
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Authors: Huanyin Chen, Yueming Xiang
Recently, Gao, Zuo and Wang introduced the $W$-weighted $m$-weak group inverse for complex matrices which generalizedthe (weighted) core-EP inverse and the WC inverse. The main purpose of this paper is to extend the concept of $W$-weighted $m$-weak group inverse for complex matrices to elements in a Banach *-algebra. This extension is called $w$-weighted $m$-generalized group inverse. We present various properties, presentations of such new weighted generalized inverse. Related (weighted) $m$-generalized core inverses are investigated as well. Many properties of the $W$-weighted $m$-weak group inverse are thereby extended to wider cases.
Comments: 22 Pages.
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[v1] 2024-06-23 13:41:03
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