The General Solutions to Some Systems of Adjointable Operator Equations

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)

Abstract

We consider two systems of adjointable operator equations \(A_{1}X=C_{1}, XB_{2}=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}\) and \(A_{1}X=C_{1}, A_{2}X=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}\) over the Hilbert \(C^{*}\)-modules. Necessary and sufficient conditions for the existence and the expressions of the general solutions to those systems are established.

Keywords

Hilbert \(C^{*}\)-modules System of operator equations General solution Inner inverse of a operator Moore–Penrose inverse of a operator 

2000 AMS subject classifications:

15A09 15A24 46L08 47A48 47A62 

Notes

Acknowledgements

This research was supported by the grants from the youth funds of Natural Science Foundation of Hebei Province (A2012403013), the Education Department Foundation of Hebei Province (QN2015218), and the Natural Science Foundation of Hebei Province (A2015403050).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Mathematics and ScienceHebei GEO UniversityShijiazhuangPeople’s Republic of China

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