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Vector Semi-Fredholm Toeplitz Operators and Mean Winding Numbers

Published online by Cambridge University Press:  11 January 2016

Dmitry Yakubovich
Dmitry Yakubovich*
Affiliation:
Departamento de Matemáticas Universidad Autónoma de Madrid and Instituto de Ciencias Matematicas CSIC-UAM-UC3M-UCM, Cantoblanco 28049, Madrid Spain dmitry.yakubovich@uam.es
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Abstract

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For a continuous nonvanishing complex-valued function g on the real line, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of det G. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.

Keywords

47B3547A5347G30

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 195 , 2009 , pp. 57 - 75
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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