Wulf Rehder, "On the product of the self-adjoint operators", International Journal of Mathematics and Mathematical Sciences, vol. 5, Article ID 473268, 4 pages, 1982. https://doi.org/10.1155/S0161171282000751
On the product of the self-adjoint operators
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.
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