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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Representation and index theory for Toeplitz operators


Author: G. J. Murphy
Journal: Trans. Amer. Math. Soc. 362 (2010), 3911-3946
MSC (2000): Primary 47B35, 46L05, 46L08, 43A17
Published electronically: March 1, 2010
MathSciNet review: 2608391
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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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Additional Information

G. J. Murphy
Affiliation: Department of Mathematics, National University of Ireland, Western Road, Cork, Ireland

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05170-6
PII: S 0002-9947(10)05170-6
Received by editor(s): January 23, 2006
Published electronically: March 1, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.