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arXiv · 1501.06983

Centre-valued index for Toeplitz operators with noncommuting symbols

John Phillips·Iain Raeburn
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Abstract

We consider an action of the real line on a C*-algebra for which there is a centre-valued invariant trace. We define a family of Toeplitz operators with symbols in the original algebra. When the symbol is invertible, the Toeplitz operator is Fredholm in an appropriate sense, and we give a formula for the index using a notion of centre-valued winding number defined using the trace. The results and techniques generalise previous results of the authors for scalar-valued traces.

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John Phillips, Iain Raeburn. 2015-01-28. Centre-valued index for Toeplitz operators with noncommuting symbols. https://doi.org/10.4153/cjm-2015-038-7

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