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 charact...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.展开更多
基金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)the Scientific and Technological Research Program Foundation of Jilin Province,China(Grant Nos.JJKH20190690KJ,20190201095JC,20200401085GX.)。
文摘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.
