A criterion for the similarity of a closed operator to a self-adjoint operator (Q1074829)

Let A be a closed linear operator in a Hilbert space H. The author obtains a criterion for the similarity of A to a selfadjoint operator T in terms of the resolvent of A. This is used to prove well-known resuls earlier obtained by Sz.-Nagy and C. Foias, I. S. Gokhberg and M. G. Krein, L. A. Sakhonovich and others involving dissipative operators, maximal dissipating operators with real spectrum, nondissipative operators. Conditions for similarity to unitary operators are also investigated.