An index theorem for Toeplitz operators on totally ordered groups

Adji, Sriwulan; Raeburn, Iain; Ströh, Anton

doi:10.1090/S0002-9939-98-04616-4

An index theorem for Toeplitz operators on totally ordered groups
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by Sriwulan Adji, Iain Raeburn and Anton Ströh PDF

Proc. Amer. Math. Soc. 126 (1998), 2993-2998 Request permission

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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