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

On the product of self-adjoint operators

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.