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Abstract The existence of a positive solution of the equation A X B = C was considered in different settings but only under additional conditions including that of regularity, as… Click to show full abstract
Abstract The existence of a positive solution of the equation A X B = C was considered in different settings but only under additional conditions including that of regularity, as well as under certain range conditions such as R ( B ) ⊆ R ( A ⁎ ) ‾ . In this paper we consider this open question and present some equivalents of the existence of a positive solution of the operator equation A X B = C without any additional range assumptions using two well-known results of Douglas and Sebestyen. Also we consider a general form of a positive solution.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
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