Geodesic
Explicit Solution to Modular Operator Equation $TXS^*-SX^*T^*=A$
Kragujevac Journal of Mathematics, Tome 40 (2016) no. 2, p. 280 .

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In this paper, by using some block operator matrix techniques, we find explicit solution of the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules. Furthermore, we solve the operator equation $TXS^* -SX^*T^*=A$, when $\rm{ran}(T)+\rm{ran}(S)$ is closed.
Classification : 47A62 15A24, 46L08
Keywords: Operator equation, Moore-Penrose inverse, Hilbert $C^*$-module 
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     author = {M. Mohammadzadeh Karizaki and M. Hassani and S. S. Dragomir},
     title = {Explicit {Solution} to {Modular} {Operator} {Equation} $TXS^*-SX^*T^*=A$},
     journal = {Kragujevac Journal of Mathematics},
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M. Mohammadzadeh Karizaki; M. Hassani; S. S. Dragomir. Explicit Solution to Modular Operator Equation $TXS^*-SX^*T^*=A$. Kragujevac Journal of Mathematics, Tome 40 (2016) no. 2, p. 280 . http://geodesic.mathdoc.fr/item/KJM_2016_40_2_a10/