Hyponormality of trigonometric Toeplitz operators

Hwang, In; Lee, Woo

doi:10.1090/S0002-9947-02-02970-7

Hyponormality of trigonometric Toeplitz operators
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by In Sung Hwang and Woo Young Lee

Trans. Amer. Math. Soc. 354 (2002), 2461-2474

DOI: https://doi.org/10.1090/S0002-9947-02-02970-7

Published electronically: February 14, 2002

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Abstract:

In this paper we establish a tractable and explicit criterion for the hyponormality of arbitrary trigonometric Toeplitz operators, i.e., Toeplitz operators $T_{\varphi }$ with trigonometric polynomial symbols $\varphi$. Our criterion involves the zeros of an analytic polynomial $f$ induced by the Fourier coefficients of $\varphi$. Moreover the rank of the selfcommutator of $T_{\varphi }$ is computed from the number of zeros of $f$ in the open unit disk $\mathbb {D}$ and in $\mathbb {C}\setminus \overline {\mathbb {D}}$ counting multiplicity.

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