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Weighted weak group inverse for Hilbert space operators

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Abstract

We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, and we extend the notation of the weighted weak group inverse for rectangular matrices. Some characterizations and representations of the weighted weak group inverse are investigated. We also apply these results to define and study the weak group inverse for a Hilbert space operator. Using the weak group inverse, we define and characterize various binary relations.

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Acknowledgements

The authors are grateful to referees for careful reading of the paper. The first author was supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174007 (451-03-68/2020-14/200124). The second author was supported by the National Natural Science Foundation of China (Grant Nos. 11901079, 61672149, 11601211) and the Scientific and Technological Research Program Foundation of Jilin Province, China (Grant Nos. JJKH20190690KJ, 20190201095JC, 20200401085GX.)

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, P. O. Box 224, 18000, Niš, Serbia

    Dijana Mosić

  2. College of Sciences, Northeast Electric Power University, Jilin, 132012, China

    Daochang Zhang

Authors
  1. Dijana Mosić
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  2. Daochang Zhang
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Correspondence to Daochang Zhang.

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Mosić, D., Zhang, D. Weighted weak group inverse for Hilbert space operators. Front. Math. China 15, 709–726 (2020). https://doi.org/10.1007/s11464-020-0847-8

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  • DOI: https://doi.org/10.1007/s11464-020-0847-8

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