# Note on the Generalized Invertibility of a-xy*

DU, FAPENG;XUE, YIFENG

• Accepted : 2014.01.29
• Published : 2015.06.23
• 15 9

#### Abstract

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

#### Keywords

Generalized inverse;Moore-Penrose inverse;Group inverse

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#### Acknowledgement

Supported by : Foundation of Xuzhou Institute of Technology