Vector semi-Fredholm Toeplitz operators and mean winding numbers

Details Vector semi-Fredholm Toeplitz operators and mean winding numbers Vector semi-Fredholm Toeplitz operators and mean winding numbers

2006-06-07

arxiv.org/abs/math/0606153v3

Nagoya Math. J. 195 (2009), 57-75

Mathematics

Functional Analysis

Third version: 17 pages. Close to the final one. TO appear in Nagoya Math. J

Scientific paper

For a continuous complex-valued function g on the real line without zeros, 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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