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Indices, characteristic numbers and essential commutants of Toeplitz operators

Kunyu Guo Department of Mathematics, Fundan University

TBD mathscidoc:1701.332933

Arkiv for Matematik, 38, (1), 97-110, 1998.6
For an essentially normal operator$T$, it is shown that there exists a unilateral shift of multiplicity$m$in$C$^{$*$}$(T)$if and only if γ($T$)≠0 and γ$(T)/m$. As application, we prove that the essential commutant of a unilateral shift and that of a bilateral shift are not isomorphic as$C$^{$*$}-algebras. Finally, we construct a natural$C$^{$*$}-algebra ε + ε_{*}on the Bergman space$L$_{$a$}^{$2$}($B$_{$n$}), and show that its essential commutant is generated by Toeplitz operators with symmetric continuous symbols and all compact operators.
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@inproceedings{kunyu1998indices,,
  title={Indices, characteristic numbers and essential commutants of Toeplitz operators},
  author={Kunyu Guo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203558331100742},
  booktitle={Arkiv for Matematik},
  volume={38},
  number={1},
  pages={97-110},
  year={1998},
}
Kunyu Guo. Indices, characteristic numbers and essential commutants of Toeplitz operators. 1998. Vol. 38. In Arkiv for Matematik. pp.97-110. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203558331100742.
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