Explicit solution of the operator equation |
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| Authors: | Dragan S Djordjevi&#x; |
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| Institution: | aDepartment of Mathematics, Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, Višegradska 33,18000 Niš, Serbia, Serbia and Montenegro |
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| Abstract: | In this paper we find the explicit solution of the equation | for linear bounded operators on Hilbert spaces, where X is the unknown operator. This solution is expressed in terms of the Moore-Penrose inverse of the operator A. Thus, results of J. H. Hodges Some matrix equations over a finite field, Ann. Mat. Pura Appl. 44 (1957) 245–550] are extended to the infinite dimensional settings.
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| Keywords: | Operator equations Moore– Penrose inverse |
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