Products of Hermitian Operators

L. J. Gray
1976 Proceedings of the American Mathematical Society  
Let A and B be selfadjoint operators on a Hilbert space. It is shown that AB and BA are not necessarily similar if their null spaces have equal dimension. If A and B are assumed to be Fredholm, then similarity can be established if additional conditions are satisfied.
doi:10.2307/2042048 fatcat:evc5chiexjhzdl4kb5iah4i64q