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.
Full-text: Open access
Permanent link to this document: http://projecteuclid.org/euclid.nmj/1252934371
Zentralblatt MATH identifier:
05611429
Nagoya Mathematical Journal