Vector semi-Fredholm Toeplitz operators and mean winding numbers
Functional Analysis
2010-12-10 v3 Complex Variables
Spectral Theory
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.
Keywords
Cite
@article{arxiv.math/0606153,
title = {Vector semi-Fredholm Toeplitz operators and mean winding numbers},
author = {Dmitry V. Yakubovich},
journal= {arXiv preprint arXiv:math/0606153},
year = {2010}
}
Comments
Third version: 17 pages. Close to the final one. TO appear in Nagoya Math. J