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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An index theorem for Toeplitz operators on the quarter-plane


Author: Adel B. Badi
Journal: Proc. Amer. Math. Soc. 137 (2009), 3779-3786
MSC (2000): Primary 47B35; Secondary 47A53, 58B15
Published electronically: June 9, 2009
MathSciNet review: 2529887
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Abstract: We prove an index theorem for Toeplitz operators on the quarter-plane using the index theory for generalized Toeplitz operators introduced by G. J. Murphy. To prove this index theorem we construct an indicial triple on the tensor product of two commutative symbol $ \mathrm{C}^\ast$-algebras. We extend our results to matrices of Toeplitz operators on the quarter-plane.


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Additional Information

Adel B. Badi
Affiliation: Department of Mathematics, Faculty of Science, The 7$^{th}$ of October University, P. O. Box 2478, Misurata, Libya
Email: adbabadi@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10007-2
PII: S 0002-9939(09)10007-2
Keywords: Toeplitz operators on the quarter-plane, generalized Fredholm index, topological index, indicial triple
Received by editor(s): February 21, 2008
Received by editor(s) in revised form: February 23, 2009
Published electronically: June 9, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.