Abstract.
We characterize hyponormal “rational” Toeplitz pairs which are pairs of Toeplitz operators whose symbols are rational functions in L∞. The main result of this article is as follows. If T = (Tϕ, Tψ) is a hyponormal rational Toeplitz pair then ϕ − βψ ∈H2 for some constant β; in other words, their co-analytic parts necessarily coincide up to a constant multiple. As a corollary we get a complete characterization of hyponormal rational Toeplitz pairs.
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The second author was supported by a grant (KRF-2008-314-C00014) from the Korea Research Foundation.
An erratum to this article is available at http://dx.doi.org/10.1007/s00020-010-1854-z.
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Hwang, I.S., Lee, W.Y. Joint Hyponormality of Rational Toeplitz Pairs. Integr. equ. oper. theory 65, 387–403 (2009). https://doi.org/10.1007/s00020-009-1729-3
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DOI: https://doi.org/10.1007/s00020-009-1729-3