Vector semi-Fredholm Toeplitz operators and mean winding numbers
arXiv:math/0606153
Abstract
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.
Third version: 17 pages. Close to the final one. TO appear in Nagoya Math. J