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Hyponormality of Toeplitz operators on the weighted Bergman space with matrix-valued circulant symbols. (English) Zbl 1512.47041

Summary: In this paper we consider the hyponormality of Toeplitz operators \(T_{\Phi}\) on the weighted Bergman space with matrix-valued circulant symbols \(\Phi\). We give a necessary and sufficient condition for the hyponormality of \(T_{\Phi}\) with such a symbol \(\Phi\) under some constraint on the entries of the matrix.

MSC:

47B20 Subnormal operators, hyponormal operators, etc.
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
42B30 \(H^p\)-spaces
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
30E05 Moment problems and interpolation problems in the complex plane
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References:

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