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Exact sequences for generalized Toeplitz operators


Author: Carl Sundberg
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0911023-1
Keywords: Toeplitz operators, semicommutator ideal
Article copyright: © Copyright 1987 American Mathematical Society

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