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Density of algebras generated by Toeplitz operators on Bergman spaces

Miroslav Engliš Mathematical Institute, Czechoslovak Academy of Sciences

TBD mathscidoc:1701.332771

Arkiv for Matematik, 30, (1), 227-243, 1991.5
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, the$C$^{*}-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant of certain shift. The result holds in Bergman spaces$A$^{2}(Ω) for a wide class of plane domains Ω⊂$C$, and in Fock spaces$A$^{2}($C$^{N}),$N$≧1.
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@inproceedings{miroslav1991density,
  title={Density of algebras generated by Toeplitz operators on Bergman spaces},
  author={Miroslav Engliš},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203537950608580},
  booktitle={Arkiv for Matematik},
  volume={30},
  number={1},
  pages={227-243},
  year={1991},
}
Miroslav Engliš. Density of algebras generated by Toeplitz operators on Bergman spaces. 1991. Vol. 30. In Arkiv for Matematik. pp.227-243. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203537950608580.
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