An index theorem for Toeplitz operators

on totally ordered groups

Authors:
Sriwulan Adji, Iain Raeburn and Anton Ströh

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2993-2998

MSC (1991):
Primary 46L55, 47B35

DOI:
https://doi.org/10.1090/S0002-9939-98-04616-4

MathSciNet review:
1473651

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that for every totally ordered group and invertible function which does not have a logarithm, there is a representation in which the Toeplitz operator is a Breuer-Fredholm operator with nonzero index; this representation is the GNS-representation associated to a natural unbounded trace on the Toeplitz algebra .

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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:
https://doi.org/10.1090/S0002-9939-98-04616-4

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

Article copyright:
© Copyright 1998
American Mathematical Society