Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-30T08:42:42.997Z Has data issue: false hasContentIssue false
  • English
  • Français

On Quasisimilarity for Analytic Toeplitz Operators

Published online by Cambridge University Press:  20 November 2018

Katsutoshi Takahashi
Katsutoshi Takahashi*
Affiliation:
Department of Mathematics, Sapporo Medical College Minami-1 Nishi-17, Sapporo, Japan
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.

Let f be a function in H∞. We show that if f is inner or if the commutant of the analytic Toeplitz operator Tf is equal to that of Tb for some finite Blaschke product b, then any analytic Toeplitz operator quasisimilar to Tf is unitarily equivalent to Tf .

Keywords

quasisimilarityanalytic Toeplitz operatorcommutant47B2047B35

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 111 - 116
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Clary, W. S., Equality of spectra of quasisimilar hyponormal operators, Proc. Amer. Math. Soc. 53 (1975), pp. 88–90.Google Scholar
2. Conway, J. B., Subnormal operators, Pitman, Boston, 1981.Google Scholar
3. Conway, J. B., On quasisimilarity for subnormal operators, IT, Canad. Math. Bull. 25 (1982), pp. 37–40.Google Scholar
4. Cowen, C. C., The commutant of an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978), pp. 1–31.Google Scholar
5. Cowen, C. C., On equivalence of Toeplitz operators, J. Operator Theory 7 (1982), pp. 167–172.Google Scholar
6. Deddens, J. A., Intertwining analytic Toeplitz operators, Michigan Math. J. 18 (1971), pp. 243–246.Google Scholar
7. Deddens, J. A., Analytic Toeplitz and composition operators, Canad. J. Math. 24 (1972), pp. 859–865.Google Scholar
8. Deddens, J. A. and Wong, T. K., The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc. 184 (1973), pp. 261–273.Google Scholar
9. Douglas, R. G., Banach algebra techniques in operator theory, Academic Press, New York, 1972.Google Scholar
10. Seddighi, K., On quasisimilarity for Toeplitz operators, Canad. Math. Bull. 28 (1985), pp. 107–112.Google Scholar
11. Sz.|-Nagy, B. and Foias, C., Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.Google Scholar
12. Sz.|-Nagy, B. and Foias, C., Jordan model for contractions of class C0 ,Acta Sci. Math. 36 (1974), pp. 305–322.Google Scholar
13. Takahashi, K., On quasiaffine transforms of unilateral shifts, Proc. Amer. Math. Soc. 100 (1987), pp. 683–687.Google Scholar
14. Thomson, J. E., The commutant of a class of analytic Toeplitz operators, II, Indiana Univ. Math. J. 25 (1976), pp. 793–800.Google Scholar
15. Wu, P. Y., Hyponormal operators quasisimilar to an isometry, Trans. Amer. Math. Soc. 291 (1985), pp. 229–239.Google Scholar
16. Wu, P. Y., Contractions quasisimilar to an isometry, preprint.Google Scholar