Mass concentration in quasicommutators of Toeplitz matrices

Authors:
Albrecht Böttcher;Jesús Gutiérrez-Gutiérrez;Pedro M. Crespo
Affiliations:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany;CEIT and Tecnun (University of Navarra), Manuel de Lardizábal 15, E-20018 San Sebastián, Spain;CEIT and Tecnun (University of Navarra), Manuel de Lardizábal 15, E-20018 San Sebastián, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 0
Cited 2

Spectral Features and Asymptotic Properties for $g$-Circulants and $g$-Toeplitz Sequences

SIAM Journal on Matrix Analysis and Applications
A note on the (regularizing) preconditioning of g-Toeplitz sequences via g-circulants

Journal of Computational and Applied Mathematics

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Abstract

We consider the algebra generated by the principal finite sections of products of multidimensional block Toeplitz operators with bounded symbols. The matrices in this algebra may be regarded as higher-dimensional cubes of increasing side length. We prove that the matrices in the quasicommutator ideal of the algebra have asymptotically no mass in the interior. This observation yields another elementary proof of first-order Szego-type results. We also determine the corners, edges, and subfaces of the cube that may carry mass asymptotically.