A criterion for the similarity of a closed operator to a self-adjoint operator
Copyright policy )A criterion for the similarity of a closed operator to a self-adjoint operator
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.
maximal dissipating operators with real spectrum, Hermitian and normal operators (spectral measures, functional calculus, etc.), closed linear operator, resolvent, Spectrum, resolvent, Linear accretive operators, dissipative operators, etc., similarity
maximal dissipating operators with real spectrum, Hermitian and normal operators (spectral measures, functional calculus, etc.), closed linear operator, resolvent, Spectrum, resolvent, Linear accretive operators, dissipative operators, etc., similarity
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