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Journal of Operator Theory

Volume 76, Issue 1, Summer 2016  pp. 171-174.

One more proof of the index formula for block Toeplitz operators

Authors:  Thomas Tradler (1), Scott O. Wilson (2), and Mahmoud Zeinalian (3)
Author institution: (1) Department of Mathematics, College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201, U.S.A.
(2) Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Flushing, NY 11367, U.S.A.
(3) Department of Mathematics, Long Island University, 720 Northern Boulevard, Brookville, NY 11548, U.S.A.

Summary:  This paper provides a new proof of the index formula for block Toeplitz operators. The idea is to calculate a certain integral formula for the winding number using Fourier series, expressing this in terms of Hankel operators, and producing the expected index.

Keywords:  index formula, winding number, Toeplitz operator

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