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Representation and index theory for Toeplitz operators
Author(s):
G.
J.
Murphy
Journal:
Trans. Amer. Math. Soc.
362
(2010),
3911-3946.
MSC (2000):
Primary 47B35, 46L05, 46L08, 43A17
Posted:
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:
10.1090/S0002-9947-10-05170-6
PII:
S 0002-9947(10)05170-6
Received by editor(s):
January 23, 2006
Posted:
March 1, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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