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Wg-Drazin-star operator and its dual

  • Dijana Mosić , Daochang Zhang EMAIL logo und Jianping Hu
Veröffentlicht/Copyright: 15. Februar 2023
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Abstract

Our goal is to define new classes of bounded linear operators between two Hilbert spaces, solving corresponding systems of equations. Precisely, we introduce the Wg-Drazin-star operator and its dual, extending the notions of the W-weighted Drazin-star matrix and its dual for a rectangular matrix. We prove many characterizations and operator matrix representations of the Wg-Drazin-star operator and its dual. As special cases of the Wg-Drazin-star operator and its dual, the g-Drazin-star operator and its dual are presented and studied. Applying our new classes of operators, we also solve adequate equations. Thus, we generalize some well-known results and present new results.


The corresponding author is supported by the National Natural Science Foundation of China (NSFC) (No. 11901079; No. 61672149), China Postdoctoral Science Foundation (No. 2021M700751), and the Scientific and Technological Research Program Foundation of Jilin Province, China (No. JJKH20190690KJ; No. 20200401085GX; No. JJKH20220091KJ).


  1. (Communicated by Gregor Dolinar )

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Received: 2021-05-25
Accepted: 2022-01-26
Published Online: 2023-02-15
Published in Print: 2023-02-23

© 2023 Mathematical Institute Slovak Academy of Sciences

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