Revista Matemática Iberoamericana

Algebras of Toeplitz operators with oscillating symbols

Albrecht Böttcher, Sergei M. Grudsky, and Enrique Ramírez de Arellano

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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

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1098885432

Mathematical Reviews number (MathSciNet)
MR2124486

Zentralblatt MATH identifier
1083.47023

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx] 37C05: Smooth mappings and diffeomorphisms 42A50: Conjugate functions, conjugate series, singular integrals 46H20: Structure, classification of topological algebras 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47L15: Operator algebras with symbol structure

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

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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