Representation and index theory for Toeplitz operators

Murphy, G.

doi:10.1090/S0002-9947-10-05170-6

Representation and index theory for Toeplitz operators
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by G. J. Murphy

Trans. Amer. Math. Soc. 362 (2010), 3911-3946

DOI: https://doi.org/10.1090/S0002-9947-10-05170-6

Published electronically: March 1, 2010

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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.

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