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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2010; 47(2): 363-372

Printed March 1, 2010

https://doi.org/10.4134/JKMS.2010.47.2.363

Copyright © The Korean Mathematical Society.

The generalized inverses $A^{(1,2)}_{T,S}$ of the adjointable operators on the Hilbert $C^*$-modules

Qingxiang Xu and Xiaobo Zhang

Shanghai Normal University and Shanghai Normal University

Abstract

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In this paper, we introduce and study the generalized inverse $A^{(1,2)}_{T,S}$ with the prescribed range $T$ and null space $S$ of an adjointable operator $A$ from one Hilbert $C^*$-module to another, and get some analogous results known for finite matrices over the complex field or associated rings, and the Hilbert space operators.

Keywords: generalized inverse, Hilbert $C^*$-module, adjointable operator

MSC numbers: Primary 15A09, 46L08

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