Explicit Solution of the Operator Equation A∗x + X∗a = B
نویسنده
چکیده
In this paper we find the explicit solution of the equation A∗X + X∗A = B for linear bounded operators on Hilbert spaces, where X is the unknown operator. This solution is expressed in terms of the MoorePenrose inverse of the operator A. Thus, results of J. H. Hodges (Ann. Mat. Pura Appl. 44 (1957) 245–550) are extended to the infinite dimensional settings. Department of Mathematics, Faculty of Sciences and Mathematics, University of Nǐs, P.O. Box 224, Vǐsegradska 33,18000 Nǐs, Serbia E-mail: [email protected] [email protected]
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