Weighted weak group inverse for Hilbert space operators

doi:10.1007/s11464-020-0847-8

Front. Math. China

2020, Vol. 15

Issue (4) : 709-726 https://doi.org/10.1007/s11464-020-0847-8

RESEARCH ARTICLE

Weighted weak group inverse for Hilbert space operators

Dijana MOSIC¹, Daochang ZHANG²(

)

¹. Faculty of Sciences and Mathematics, University of Ni_s; P. O. Box 224, 18000 Ni_s; Serbia
². College of Sciences, Northeast Electric Power University, Jilin 132012, China

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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.

Keywords Weak group inverse weighted core-EP inverse Wg-Drazin inverse Hilbert space

Corresponding Author(s): Daochang ZHANG

Issue Date: 09 September 2020

Cite this article:

Dijana MOSIC,Daochang ZHANG. Weighted weak group inverse for Hilbert space operators[J]. Front. Math. China, 2020, 15(4): 709-726.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0847-8
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I4/709

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