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Common Hermitian and positive solutions to the adjointable operator equations $$AX = C$$, $$XB = D$$. (English) Zbl 1153.47012
The author extends and corrects some results from [A. Dajić and J. J. Koliha, J. Math, Anal. Appl. 333, No. 2, 567–576 (2007; Zbl 1120.47009)], where positive common solutions $$X$$ were found for the equations in the title within the framework of $$C^*$$-algebras. Working in the more general setting of Hilbert $$C^*$$-modules, the author of the present paper provides necessary and sufficient conditions for the existence of common Hermitian and positive solutions $$X$$ to the above equations.

##### MSC:
 47A62 Equations involving linear operators, with operator unknowns 46L08 $$C^*$$-modules 15A09 Theory of matrix inversion and generalized inverses 15A24 Matrix equations and identities
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##### References:
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