Abstract
We give necessary and sufficient conditions for the existence of the common positive solution to the equations A1X1=C1,X1B1=D1,A2X2=C2,X2B2=D2,A3X1A3∗+A4X2A4∗=C5 for adjointable operators between Hilbert C∗-modules, and present an expression of the positive solution to the system when the solvability conditions are satisfied. As an application, we consider the reflexive positive semidefinite solution to the system of complex matrix equations AX=B,XC=D,EXE∗=F.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.