Real positive solutions of operator equations $ AX = C $ and $ XB = D $
Authors:
Open Access
- 1 January 2023
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 8 (7) , 15214-15231
Abstract
In this paper, we mainly consider operator equations $ AX = C $ and $ XB = D $ in the framework of Hilbert space. A new representation of the reduced solution of $ AX = C $ is given by a convergent operator sequence. The common solutions and common real positive solutions of the system of two operator equations $ AX = C $ and $ XB = D $ are studied. The detailed representations of these solutions are provided which extend the classical closed range case with a short proof.
Keywords
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