Two Equal Range Operators on Hilbert $C^*$-modules
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)Publication Date: 2021-05-01
Authors : Ali Reza Janfada; Javad Farokhi-Ostad;
Page : 85-96
Keywords : Closed range; Moore-Penrose inverse; Hilbert $C^*$-module;
Abstract
In this paper, number of properties, involving invertibility, existence of Moore-Penrose inverse and etc for modular operators with the same ranges on Hilbert $C^*$-modules are presented. Natural decompositions of operators with closed range enable us to find some relations of the product of operators with Moore-Penrose inverses under the condition that they have the same ranges in Hilbert $C^*$-modules. The triple reverse order law and the mixed reverse order law in the special cases are also given. Moreover, the range property and Moore-Penrose inverse are illustrated.
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Last modified: 2021-11-03 14:32:34