Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Essentially subnormal operators and $ K$-spectral sets

Author: Ridgley Lange
Journal: Proc. Amer. Math. Soc. 88 (1983), 449-453
MSC: Primary 47A15; Secondary 47B20
MathSciNet review: 699412
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] L. G. Brown, R. G. Douglas and P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of $ {C^*}$-algebras, Proc. Conf. Operator Theory, Lecture Notes in Math., vol. 345, Springer, 1973. MR 0380478 (52:1378)
  • [2] J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839-873. MR 0005790 (3:208c)
  • [3] K. R. Davidson and C.-K. Fong, An algebra which is not closed in the Calkin algebra, Pacific J. Math. 72 (1977), 57-58. MR 0463931 (57:3869)
  • [4] P. A. Fillmore, J. G. Stampfli and J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179-192. MR 0322534 (48:896)
  • [5] R. F. Olin, Functional relationships between a subnormal operator and its minimal normal extension, Pacific J. Math 63 (1976), 221-229. MR 0420324 (54:8338)
  • [6] J. G. Stampfli, Compact perturbations, normal eigenvalues, and a problem of Salinas, J. London Math. Soc. 9 (1974), 165-175. MR 0365196 (51:1449)
  • [7] -, An extension of Scott Brown's subspace theorem:$ K$-spectral sets, J. Operator Theory 3 (1980), 3-21.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A15, 47B20

Retrieve articles in all journals with MSC: 47A15, 47B20

Additional Information

Keywords: Essentially subnormal operators, $ K$-spectral set, invariant subspace
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society