Arkiv för Matematik

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

Indices, characteristic numbers and essential commutants of Toeplitz operators

Kunyu Guo

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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.


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

Article information

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

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

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2000 © Institut Mittag-Leffer


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

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