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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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