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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyponormality of Toeplitz operators
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by Carl C. Cowen
Proc. Amer. Math. Soc. 103 (1988), 809-812
DOI: https://doi.org/10.1090/S0002-9939-1988-0947663-4

Abstract:

For $\varphi$ in ${L^\infty }(\partial {\mathbf {D}})$, let $\varphi = f + \bar g$ where $f$ and $g$ are in ${H^2}$. In this note, it is shown that the Toeplitz operator $T\varphi$ is hyponormal if and only if $g = c + {T_{\bar h}}f$ for some constant $c$ and some function $h$ in ${H^\infty }({\mathbf {D}})$ with ${\left \| h \right \|_\infty } \leq 1$.
References
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 809-812
  • MSC: Primary 47B35; Secondary 47B20
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0947663-4
  • MathSciNet review: 947663