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The Index Theory Associated to a Non-Finite Trace on a C*-Algebra

Published online by Cambridge University Press:  20 November 2018

G. J. Murphy
G. J. Murphy*
Affiliation:
Department of Mathematics, National University of Ireland, Cork, Western Road, Cork, Ireland email: gjm@ucc.ie
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Abstract

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The index theory considered in this paper, a generalisation of the classical Fredholm index theory, is obtained in terms of a non-finite trace on a unital ${{C}^{*}}$ -algebra. We relate it to the index theory of M. Breuer, which is developed in a von Neumann algebra setting, by means of a representation theorem. We show how our new index theory can be used to obtain an index theorem for Toeplitz operators on the compact group $\text{U}\left( 2 \right)$ , where the classical index theory does not give any interesting result.

Keywords

46L47B3547L80

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 251 - 259
Copyright
Copyright © Canadian Mathematical Society 2005

References

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