Note on the Generalized Invertibility of a-xy*

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.251-258
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.251
Title & Authors
Note on the Generalized Invertibility of a-xy*
DU, FAPENG; XUE, YIFENG;

Abstract
Let $\small{\mathcal{A}}$ be a unital $\small{C^*}$-algebra, a, x and y are elements in $\small{\mathcal{A}}$. In this paper, we present the expression of the Moore-Penrose inverse and the group inverse of a-$\small{xy^*}$ under the conditions $\small{x=aa^+x,y^*=y^*a^+a}$, respectively.
Keywords
Generalized inverse;Moore-Penrose inverse;Group inverse;
Language
English
Cited by
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