Revista Matemática Iberoamericana


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Volume 20, Issue 3, 2004, pp. 647–671
DOI: 10.4171/RMI/404

Published online: 2004-12-31

Algebras of Toeplitz operators with oscillating symbols

Albrecht Böttcher[1], Alexander Poznyak[2] and Enrique Ramírez de Arellano[3]

(1) Technische Universität Chemnitz, Germany
(2) CINVESTAV del IPN, Mexico, D.F., Mexico
(3) CINVESTAV del IPN, Mexico, D.F., Mexico

This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form $b(e^{i\alpha(x)})$ where $b$ belongs to some algebra of functions on the unit circle and $\alpha$ is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.

Keywords: Toeplitz operator, Banach algebra, $C^*$-algebra, Fredholm operator, normally solvable operator

Böttcher Albrecht, Poznyak Alexander, Ramírez de Arellano Enrique: Algebras of Toeplitz operators with oscillating symbols. Rev. Mat. Iberoam. 20 (2004), 647-671. doi: 10.4171/RMI/404