Electronic Journal of Linear Algebra, ( ISI ), Volume (34), No (1), Year (2018-8) , Pages (381-388)

Title : ( Positive solutions of the system of operator equations $A_1X=C_1,XA_2=C_2‎, ‎A_3XA^*_3=C_3‎, ‎A_4XA^*_4=C_4$ in Hilbert $C^*$-modules )

Authors: R. Eskandari , X. Fang , Mohammad Sal Moslehian , Q. Xu ,
File:

Access to full-text not allowed by authors

Citation: BibTeX | EndNote

Abstract

‎We give necessary and sufficient conditions for the operator system $A_1X=C_1‎, ‎XA_2=C_2‎, ‎A_3XA^*_3=C_3,$ and $ A_4XA^*_4=C_4$ to have a common positive solution‎, ‎where $A_i$'s and $C_i$'s are adjointable operators on Hilbert $C^*$-modules‎. ‎This corrects a published result by removing some gaps in its proof‎. ‎Finally we give a technical example and show that our investigation in the setting of Hilbert $C^*$-modules is different from that of Hilbert spaces‎.

Keywords

, Hilbert $C^*$, module; Operator equation; Orthogonally complemented submodule