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On unbounded hyponormal operators. (English) Zbl 0684.47020

A (not necessarily bounded) linear operator T on a Hilbert space is called hyponormal, if \({\mathcal D}(T)\subset {\mathcal D}(T^*)\) and \(\| T^*x\| \leq \| Tx\|\) for \(x\in {\mathcal D}(T)\). After the statement of elementary properties hyponormal operators with spectrum contained in an angle are studied with respect to the generated semigroups and accretivity. For some differential operators and for composition operators in \(L^ 2(\mu)\) conditions implying hyponormality are given.
Reviewer: G.Garske

MSC:

47B20 Subnormal operators, hyponormal operators, etc.
47D03 Groups and semigroups of linear operators
47E05 General theory of ordinary differential operators
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[1] Clancey, K.,Seminormal Operators, Lecture Notes Mathematics 742, Springer-Verlag, Berlin etc., 1981. · Zbl 0435.47032
[2] Clary, S., Equality of spectra of quasisimilar hyponormal operators,Proc. Amer. Math. Soc. 53 (1975), 88–90. · Zbl 0317.47014
[3] von Casteren, J. A.,Generators of continuous semi-groups, Pitman Research Notes in Math. 115, Pitman, 1985.
[4] Janas, J., Inductive limit of operators and its applications,Studia Math. 90 (1988) 87–102. · Zbl 0661.47027
[5] McIntosh, A., Operators which haveH functional calculus,Proc. Centre Math. Analysis Austr. Nat. University 14, pp. 210–231, Austral. Nat. Univ. Canberra, 1986.
[6] Kato, T. Perturbation theory for linear operators, Springer-Verlag, Berlin etc. 1966. · Zbl 0148.12601
[7] Reed, M. andSimon, B.,Methods of modern mathematical physics, Vol. II, Academic Press, New York, 1975.
[8] Stochel, J. B., Subnormality and generalized commutation relations,Glasgow Math. J.30 (1988) 259–262. · Zbl 0656.47015
[9] Stochel, J. andSzafraniec, F. H., On normal extensions of unbounded operators I,J. Operator Theory 14 (1985), 31–55. · Zbl 0613.47022
[10] Šubin, M. A.,Pseudodifferential operators, Moscow, Mir 1978 (in Russian).
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