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

• Autores: G. J. Murphy
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 2, 2005, págs. 251-259
• Idioma: inglés
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• Resumen

  • 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 mathbf{U}(2), where the classical index theory does not give any interesting result.