Essentially subnormal operators and $K$-spectral sets
HTML articles powered by AMS MathViewer
- by Ridgley Lange PDF
- Proc. Amer. Math. Soc. 88 (1983), 449-453 Request permission
Abstract:
Let $T$ be an essentially subnormal operator. We give six conditions which are equivalent to the spectrum of $T$ being a $K$-spectral set. From this follow two corollaries which give sufficient conditions for invariant subspaces of essentially subnormal operators. Several examples are given that show that some essentially subnormal operators are not essentially normal nor perturbations of subnormal operators.References
- L. G. Brown, R. G. Douglas, and P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of $C^{\ast }$-algebras, Proceedings of a Conference on Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Lecture Notes in Math., Vol. 345, Springer, Berlin, 1973, pp. 58–128. MR 0380478
- J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839–873. MR 5790, DOI 10.2307/1968771
- K. R. Davidson and C. K. Fong, An operator algebra which is not closed in the Calkin algebra, Pacific J. Math. 72 (1977), no. 1, 57–58. MR 463931, DOI 10.2140/pjm.1977.72.57
- P. A. Fillmore, J. G. Stampfli, and J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179–192. MR 322534
- Robert F. Olin, Functional relationships between a subnormal operator and its minimal normal extension, Pacific J. Math. 63 (1976), no. 1, 221–229. MR 420324, DOI 10.2140/pjm.1976.63.221
- Joseph G. Stampfli, Compact perturbations, normal eigenvalues and a problem of Salinas, J. London Math. Soc. (2) 9 (1974/75), 165–175. MR 365196, DOI 10.1112/jlms/s2-9.1.165 —, An extension of Scott Brown’s subspace theorem:$K$-spectral sets, J. Operator Theory 3 (1980), 3-21.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 449-453
- MSC: Primary 47A15; Secondary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1983-0699412-0
- MathSciNet review: 699412