|
|||||
|
|
Explicit solution of the operator equation |
|
| Authors: | Dragan S. Djordjevi&#x |
| Affiliation: | aDepartment of Mathematics, Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, Višegradska 33,18000 Niš, Serbia, Serbia and Montenegro |
| Abstract: | 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 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.
| Keywords: | Operator equations Moore– Penrose inverse |
| 本文献已被 ScienceDirect 等数据库收录！ | |