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On a class of jointly hyponormal Toeplitz operators

Authors:	Caixing Gu

Institution:	Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407

Abstract:	We characterize when a pair of Toeplitz operators $\mathbf{T}=(T_{\phi },T_{\psi})$ is jointly hyponormal under various assumptions--for example, $\phi$ is analytic or $\phi$ is a trigonometric polynomial or $\phi-\psi$ is analytic. A typical characterization states that $\mathbf{T}=(T_{\phi },T_{\psi})$ is jointly hyponormal if and only if an algebraic relation of $\phi$ and $\psi$ holds and the single Toeplitz operator $T_{\omega}$ is hyponormal, where $\omega$ is a combination of $\phi$ and $\psi$ . More general results for an -tuple of Toeplitz operators are also obtained.

Keywords:	Toeplitz operator Hankel operator joint hyponormality

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