International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 34, Pages 2157-2176
doi:10.1155/S0161171203107107
Block Toeplitz operators with frequency-modulated semi-almost periodic symbols
A. Böttcher1
, S. Grudsky2
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
Abstract
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.