Toeplitz operators with piecewise continuous symbols on the Hardy space H1

Santeri Miihkinen Åbo Akademi University Jani Virtanen University of Reading

Functional Analysis mathscidoc:1912.43045

Arkiv for Matematik, 57, (2), 429 – 435, 2019
The geometric descriptions of the (essential) spectra of Toeplitz operators with piecewise continuous symbols are among the most beautiful results about Toeplitz operators on Hardy spaces Hp with 1<p<∞. In the Hardy space H1, the essential spectra of Toeplitz operators are known for continuous symbols and symbols in the Douglas algebra C+H∞. It is natural to ask whether the theory for piecewise continuous symbols can also be extended to H1. We answer this question in the negative and show in particular that the Toeplitz operator is never bounded on H1 if its symbol has a jump discontinuity.
Toeplitz operators, Hardy spaces, Fredholm properties, essential spectrum, piecewise continuous symbols
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@inproceedings{santeri2019toeplitz,
  title={Toeplitz operators with piecewise continuous symbols on the Hardy space H1},
  author={Santeri Miihkinen, and Jani Virtanen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204142140027243601},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={2},
  pages={429 – 435},
  year={2019},
}
Santeri Miihkinen, and Jani Virtanen. Toeplitz operators with piecewise continuous symbols on the Hardy space H1. 2019. Vol. 57. In Arkiv for Matematik. pp.429 – 435. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204142140027243601.
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