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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 813-816
http://dx.doi.org/10.1155/S0161171282000751

On the product of the self-adjoint operators

Department of Mathematics and Computer Science, University of Denver, Denver 80208, Colorado, USA

Received 19 April 1982

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the positivity requirement cannot be dropped.