### SOLUTIONS FOR THE MIXED SYLVESTER OPERATOR EQUATIONS

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#### Abstract

This paper is devoted to investigating some system of mixed coupled generalized Sylvester operator equations. The block operator matrix decomposition is used to find the necessary and sufficient conditions for the solvability to these systems. The solutions of the system are expressed in terms of the Moore--Penrose inverses of the coefficient operators.

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DOI: https://doi.org/10.22190/FUMI201118062F

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