The solutions to some operator equations in Hilbert $C^*$-module

Journal of Linear and Topological Algebra

مقاله 4، دوره 04، شماره 01، اردیبهشت 2015، صفحه 35-42   

نوع مقاله: Research Paper

نویسندگان

M. Mohammadzadeh Karizaki؛ M. Hassani^*

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

چکیده

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we find explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

کلیدواژه‌ها

Operator equation؛ Moore-Penrose inverse؛ Complemented submodule, Closed range, Hilbert C*-module

مراجع

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