## Revista Matemática Iberoamericana

### Algebras of Toeplitz operators with oscillating symbols

#### Abstract

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.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 20, Number 3 (2004), 647-671.

Dates
First available in Project Euclid: 27 October 2004

https://projecteuclid.org/euclid.rmi/1098885432

Mathematical Reviews number (MathSciNet)
MR2124486

Zentralblatt MATH identifier
1083.47023

#### Citation

Böttcher, Albrecht; Grudsky, Sergei M.; Ramírez de Arellano, Enrique. Algebras of Toeplitz operators with oscillating symbols. Rev. Mat. Iberoamericana 20 (2004), no. 3, 647--671. https://projecteuclid.org/euclid.rmi/1098885432

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