Exact sequences for generalized Toeplitz operators
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- by Carl Sundberg PDF
- Proc. Amer. Math. Soc. 101 (1987), 634-636 Request permission
Abstract:
Let $\mathcal {T}$ be the ${C^*}$-algebra generated by the Toeplitz operators on ${H^2}$ of the unit circle, and let $C$ be the $\mathcal {T}$-ideal generated by $\{ {T_\varphi }{T_\psi } - {T_{\varphi \psi }}:\varphi ,\psi \in {L^\infty }\}$. It is well known that $\mathcal {T} / C$ is naturally $*$-isomorphic to ${L^\infty }$. Several authors have obtained a similar result for other classes of Toeplitz operators. In the present paper a general theorem is proved which establishes the relevant isomorphism for a wide class of generalized Toeplitz operators.References
- L. A. Coburn, Singular integral operators and Toeplitz operators on odd spheres, Indiana Univ. Math. J. 23 (1973/74), 433–439. MR 322595, DOI 10.1512/iumj.1973.23.23036
- A. M. Davie and N. P. Jewell, Toeplitz operators in several complex variables, J. Functional Analysis 26 (1977), no. 4, 356–368. MR 0461195, DOI 10.1016/0022-1236(77)90020-9
- Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893
- William W. Hastings, A Carleson measure theorem for Bergman spaces, Proc. Amer. Math. Soc. 52 (1975), 237–241. MR 374886, DOI 10.1090/S0002-9939-1975-0374886-9
- Kenneth Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74–111. MR 215102, DOI 10.2307/1970361
- G. McDonald and C. Sundberg, Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), no. 4, 595–611. MR 542947, DOI 10.1512/iumj.1979.28.28042
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 634-636
- MSC: Primary 47B35; Secondary 47D25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0911023-1
- MathSciNet review: 911023