On Quasisimilarity for Analytic Toeplitz Operators
Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 111-116

Voir la notice de l'article provenant de la source Cambridge University Press

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 .
DOI : 10.4153/CMB-1988-017-7
Mots-clés : quasisimilarity, analytic Toeplitz operator, commutant, 47B20, 47B35
Takahashi, Katsutoshi. On Quasisimilarity for Analytic Toeplitz Operators. Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 111-116. doi: 10.4153/CMB-1988-017-7
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[1] 1. Clary, W. S., Equality of spectra of quasisimilar hyponormal operators, Proc. Amer. Math. Soc. 53 (1975), pp. 88–90. Google Scholar

[2] 2. Conway, J. B., Subnormal operators, Pitman, Boston, 1981. Google Scholar

[3] 3. Conway, J. B., On quasisimilarity for subnormal operators, IT, Canad. Math. Bull. 25 (1982), pp. 37–40. Google Scholar

[4] 4. Cowen, C. C., The commutant of an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978), pp. 1–31. Google Scholar

[5] 5. Cowen, C. C., On equivalence of Toeplitz operators, J. Operator Theory 7 (1982), pp. 167–172. Google Scholar

[6] 6. Deddens, J. A., Intertwining analytic Toeplitz operators, Michigan Math. J. 18 (1971), pp. 243–246. Google Scholar

[7] 7. Deddens, J. A., Analytic Toeplitz and composition operators, Canad. J. Math. 24 (1972), pp. 859–865. Google Scholar

[8] 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] 9. Douglas, R. G., Banach algebra techniques in operator theory, Academic Press, New York, 1972. Google Scholar

[10] 10. Seddighi, K., On quasisimilarity for Toeplitz operators, Canad. Math. Bull. 28 (1985), pp. 107–112. Google Scholar

[11] 11. Sz.|-Nagy, B. and Foias, C., Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970. Google Scholar

[12] 12. Sz.|-Nagy, B. and Foias, C., Jordan model for contractions of class C ,Acta Sci. Math. 36 (1974), pp. 305–322. Google Scholar

[13] 13. Takahashi, K., On quasiaffine transforms of unilateral shifts, Proc. Amer. Math. Soc. 100 (1987), pp. 683–687. Google Scholar

[14] 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] 15. Wu, P. Y., Hyponormal operators quasisimilar to an isometry, Trans. Amer. Math. Soc. 291 (1985), pp. 229–239. Google Scholar

[16] 16. Wu, P. Y., Contractions quasisimilar to an isometry, preprint. Google Scholar

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