Document Type : Research Paper

Authors

• Mehdi Mohammadzadeh Karizaki ¹
• Mahmoud Hassani ²
• Dragan Djordjevic ³

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 $TX{S}^{\ast }-S{X}^{\ast }{T}^{\ast }=A$ in the general setting of the adjointable operators between Hilbert $C^{\ast }$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.

Keywords

• Operator equation
• Moore-Penrose inverse
• Hilbert $C^{\ast }$-module