The solutions to some operator equations in Hilbert $C^*$-module
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Abstract:
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 nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.
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Journal title
volume 04 issue 01
pages 35- 42
publication date 2015-04-01
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