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REPRESENTATION AND INDEX THEORY FOR TOEPLITZ OPERATORS

By G. J. Murphy

Abstract

Abstract. We study Toeplitz operators on the Hardy spaces of connected compact abelian groups and of tube-type bounded symmetric domains. A representation theorem for these operators and for classes of abstract Toeplitz elements in C*-algebras is proved. This is used to give a unified treatment to index theory in this setting, and a variety of new index theorems are proved that generalize the Gohberg–Krein theorem for Toeplitz operators on the Hardy space of the unit circle in the plane. 1

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.163.6662
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