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Published online by Cambridge University Press: 11 January 2016
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.