International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 34, Pages 2157-2176

Block Toeplitz operators with frequency-modulated semi-almost periodic symbols

A. Böttcher,1 S. Grudsky,2 and I. Spitkovsky3

1Fakultät für Mathematik, TU Chemnitz, Chemnitz 09107, Germany
2Departamento de Matematicas, CINVESTAV del IPN, Aportado Postal 14-740, México, DF, 07360, Mexico
3Department of Mathematics, The College of William and Mary, Williamsburg 23187-8795, VA, USA

Received 23 July 2001; Revised 19 February 2002

Copyright © 2003 A. Böttcher et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the influence of frequency modulation on the semi-Fredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphism α of the real line that ensure the following: if b belongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix functions) and the Toeplitz operator generated by the matrix function b(x) is semi-Fredholm, then the Toeplitz operator with the matrix symbol b(α(x)) is also semi-Fredholm.