Abstract
In this note we consider joint hyponormality of pairs of Toeplitz operators acting on the Hardy space \({H^2(\mathbb T)}\) of the unit circle \({\mathbb T}\). We give answers on some questions which arise from joint hyponormality of Toeplitz pairs with rational symbols.
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Abrahamse M.B.: Sunormal Toeplitz operators and functions of bounded type. Duke Math. J. 43, 597–604 (1976)
Athavale A.: On joint hyponormality of operators. Proc. Am. Math. Soc. 103, 417–423 (1988)
Bram J.: Sunormal operators. Duke Math. J. 22, 75–94 (1955)
Conway, J.B.: The Theory of Subnormal Operators, Mathematical Surveys and Monographs, vol. 36, American Mathematical Society, Providence (1991).
Conway J.B., Szymanski W.: Linear combination of hyponormal operators. Rocky Mt. J. Math. 18, 695–705 (1988)
Cowen C.: On equivalnce of Toeplitz operators. J. Oper. Theory 7, 167–172 (1982)
Cowen C.: Hyponormality of Toeplitz operators. Proc. Am. Math. Soc. 103, 809–812 (1988)
Curto, R.E.: Joint hyponormality: a bridge between hyponormality and subnormality. Operator theory: operator algebras and applications (Durham, NH, 1988). In: Arveson, W.B., Douglas, R.G., (eds.) Proceedings of Symposia in Pure Mathematics, vol. 51, Part II, American Mathematical Social Providence, pp. 69–91 (1991)
Curto, R.E., Lee, W.Y.: Joint hyponormality of Toeplitz pairs. Memoirs of the American Mathematical Society, vol. 712, American Mathematical Social Providence (2001)
Curto, R.E., Muhly, P.S., Xiam, J.: Hyponormal pairs of commuting operators. Contributions to Operator Theory and Its Applications (Mesa, AZ, 1987). In: Gohberg, I., Helton, J.W., Rodman, L. (eds.) Operator Theory: Advances and Applications, vol. 35, pp. 1–22. Birkhäuser, Basel (1988)
Douglas R.G., Paulsen V.I., Yan K.: Operator theory and algebraic geometry. Bull. Am. Math. Soc. (N.S.) 20, 67–71 (1989)
Douglas R.G., Yan K.: A multi-variable Berger-Shaw theorem. J. Oper. Theory 27, 205–217 (1992)
Farenick D.R., McEachin R.: Toeplitz operators hyponormal with the unilateral shift. Integral Equ. Oper. Theory 22, 273–280 (1995)
Gu C.: On a class of jointly hyponormal Toeplitz operators. Trans. Am. Math. Soc. 354, 3275–3298 (2002)
Hwang, I.S., Lee, W.Y.: Joint hyponormality of rational Toeplitz pairs. Integral Equ. Oper. Theory 65, 387–403 (2009). Erratum 69, 445–446 (2011)
McCullough S., Paulsen V.: A note on joint hyponormality. Proc. Am. Math. Soc. 107, 187–195 (1989)
McCullough S., Paulsen V.: k-hyponormality of weighted shifts. Proc. Am. Math. Soc. 116, 165–169 (1992)
Nikolskii, N.K.: Treatise on the shift operator. Springer, New York (1986)
Xia D.: On the semi-hyponormal n-tuple of operators. Integral Equ. Oper. Theory 6, 879–898 (1983)
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Hwang, I.S., Kim, A.H. Joint Hyponormality of Toeplitz Pairs with Rational Symbols. Integr. Equ. Oper. Theory 79, 123–134 (2014). https://doi.org/10.1007/s00020-014-2132-2
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DOI: https://doi.org/10.1007/s00020-014-2132-2