The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules

Document Type: Research Paper

Authors

1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran

2 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

3 D. S. Djordjevic, Faculty of Sciences and Mathematics, University of ´ Nis, Visegradska 33, P.O. Box 224, 18000 Nis, Serbia.

Abstract

In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.

Keywords