Vector semi-Fredholm Toeplitz operators and mean winding numbers
Dmitry Yakubovich
Source: Nagoya Math. J. Volume 195
(2009), 57-75.
Abstract
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.
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Mathematical Reviews number (MathSciNet): MR2552953
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