Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T14:29:07.191Z Has data issue: false hasContentIssue false
  • English
  • Français

A Subnormal Operator and its Dual

Published online by Cambridge University Press:  20 November 2018

Robert F. Olin  and
Liming Yang
Robert F. Olin
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virgina 24061, U.S.A.
Liming Yang
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virgina 24061, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.

Keywords

42B2030H05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 381 - 396
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Conway, J., The dual of a subnormal operator, J. Operator Theory, 5 (1981), 195–211.Google Scholar
2. Conway, J., Subnormal operators, Pitman, Boston, 1981.Google Scholar
3. Conway, J., The theory of subnormal operators, Math. Surveys and Monographs 36, 1991.Google Scholar
4. Gamelin, T.W., Uniform algebras, Prentice Hall Englewood Cliffs, New Jersey, 1969.Google Scholar
5. Gamelin, T.W., Russo, P. and Thomson, J.E., A Stone-Weierstrass theorem for weak star approximation by rational functions, J. Funct. Anal 87 (1989), 170–176.Google Scholar
6. Murphy, G.J., Self-dual subnormal operators, Comment. Math. Univ. Carolin. 23 (1982), 467–473.Google Scholar
7. Olin, R. and Thomson, J., Some index theorems for subnormal operators, J. Operator Theory, 3 (1980), 115–142.Google Scholar
8. Olin, R. and Yang, L., Z/(/x), J. Funct. Anal., 134 (1995) 297-300.Google Scholar
9. Thomson, J., Approximation in the mean by polynomials, Ann. of Math. 133 (1991), 477—507.Google Scholar
10. Yan, K., U-selfadjoint operators and self-dual subnormal operators, J. Fudan Univ. Natur. Sci. 24 (1985), 459–463.Google Scholar