The solutions to some operator equations in Hilbert $C^*$-module
الموضوعات :M. Mohammadzadeh Karizaki 1 , M. Hassani 2
1 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
الکلمات المفتاحية: Operator equation, Moore-Penrose inverse, Complemented submodule, Closed range, Hilbert C*-module,
ملخص المقالة :
In this paper, we state some results on product of operators with closed rangesand we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of theadjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by usingsome block operator matrix techniques, we find explicit solution of the operator equation$TXS^*-SX^*T^*= A$.
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