## On a class of jointly hyponormal Toeplitz operators

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## 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 $n$-tuple of Toeplitz operators are also obtained.## References

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## Additional Information

**Caixing Gu**- Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
- MR Author ID: 236909
- ORCID: 0000-0001-6289-7755
- Email: cgu@calpoly.edu
- Received by editor(s): December 28, 1999
- Received by editor(s) in revised form: February 9, 2001, and December 3, 2001
- Published electronically: April 3, 2002
- Additional Notes: Partially supported by the National Science Foundation Grant DMS-9706838.
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 3275-3298 - MSC (2000): Primary 47B35, 47B20
- DOI: https://doi.org/10.1090/S0002-9947-02-03001-5
- MathSciNet review: 1897400