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Proceedings of the American Mathematical Society

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

 

 

Hyponormality of Toeplitz operators


Author: Carl C. Cowen
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
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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\Vert h \right\Vert _\infty } \leq 1$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947663-4
Keywords: Toeplitz operator, subnormal operator
Article copyright: © Copyright 1988 American Mathematical Society