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 acute; 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

Volume 7, Issue 2 - Serial Number 2
December 2016
Pages 127-132
  • Receive Date: 19 November 2015
  • Revise Date: 24 June 2016
  • Accept Date: 07 October 2016