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Solutions to a class of operator equations. (Chinese. English summary) Zbl 1255.47019

Summary: With the help of block operator matrix, sufficient and necessary conditions for the existence of solutions to the operator equation \({AXB}^*+{BX}^*{A}^*={C}\) and the representation of solutions are established. Especially, when \({B}\) is an orthogonal projection \({P}\), sufficient and necessary conditions for the existence of solutions to the operator equation \({AXP}+{PX}^*{A}^*={C}\) and the representation of solutions are also given.

MSC:

47A62 Equations involving linear operators, with operator unknowns
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