Arkiv för Matematik

  • Ark. Mat.
  • Volume 38, Number 1 (2000), 97-110.

Indices, characteristic numbers and essential commutants of Toeplitz operators

Kunyu Guo

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Abstract

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 ${}_{a}^{2}$ (Bn), and show that its essential commutant is generated by Toeplitz operators with symmetric continuous symbols and all compact operators.

Note

Supported by NSFC and Laboratory of Mathematics for Nonlinear Science at Fudan University.

Article information

Source
Ark. Mat., Volume 38, Number 1 (2000), 97-110.

Dates
Received: 30 June 1998
Revised: 15 December 1998
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898669

Digital Object Identifier
doi:10.1007/BF02384493

Mathematical Reviews number (MathSciNet)
MR1749361

Zentralblatt MATH identifier
1021.47018

Rights
2000 © Institut Mittag-Leffer

Citation

Guo, Kunyu. Indices, characteristic numbers and essential commutants of Toeplitz operators. Ark. Mat. 38 (2000), no. 1, 97--110. doi:10.1007/BF02384493. https://projecteuclid.org/euclid.afm/1485898669


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