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Essentially hyponormal multiplication operators on the Dirichlet space

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Abstract

On the Dirichlet space D, we show that there is a multiplier f of D such that \(M_f\) is not essentially hyponormal, i.e. \(\pi (M_f)\) is not hyponormal in the Calkin algebra \(B(D)/\mathcal {K}(D)\).

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Shuaibing Luo

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  1. Shuaibing Luo
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Correspondence to Shuaibing Luo.

Additional information

This work is supported by the Young Teacher Program of Hunan University. The author would like to thank Professor Stefan Richter for some useful conversations.

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Luo, S. Essentially hyponormal multiplication operators on the Dirichlet space. Arch. Math. 108, 283–291 (2017). https://doi.org/10.1007/s00013-016-1006-z

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  • DOI: https://doi.org/10.1007/s00013-016-1006-z

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