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An index theorem for Toeplitz operators on totally ordered groups

Author(s): Sriwulan Adji; Iain Raeburn; Anton Ströh
Journal: Proc. Amer. Math. Soc. 126 (1998), 2993-2998.
MSC (1991): Primary 46L55, 47B35
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Abstract: We show that for every totally ordered group $\Gamma$ and invertible function $f\in C(\widehat\Gamma)$ which does not have a logarithm, there is a representation in which the Toeplitz operator $T_f$ is a Breuer-Fredholm operator with nonzero index; this representation is the GNS-representation associated to a natural unbounded trace on the Toeplitz algebra $\mathcal T(\Gamma)$.

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Additional Information:

Sriwulan Adji
Affiliation: Department of Mathematics, Institut Teknologi Bandung, Ganesha 10, Bandung 40132, Indonesia

Iain Raeburn
Affiliation: Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
Email: iain@frey.newcastle.edu.au

Anton Ströh
Affiliation: Department of Mathematics, University of Pretoria, 0002 Pretoria, South Africa

DOI: 10.1090/S0002-9939-98-04616-4
PII: S 0002-9939(98)04616-4
Keywords: Totally ordered group, Toeplitz operator, Toeplitz algebra, trace, Breuer-Fredholm index
Received by editor(s): January 13, 1997
Received by editor(s) in revised form: March 11, 1997
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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