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
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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