JournalsrmiVol. 20, No. 3pp. 647–671

Algebras of Toeplitz operators with oscillating symbols

  • Albrecht Böttcher

    Technische Universität Chemnitz, Germany
  • Alexander Poznyak

    CINVESTAV del IPN, Mexico, D.F., Mexico
  • Enrique Ramírez de Arellano

    CINVESTAV del IPN, Mexico, D.F., Mexico
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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(eiα(x))b(e^{i\alpha(x)}) where bb belongs to some algebra of functions on the unit circle and α\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.

Cite this article

Albrecht Böttcher, Alexander Poznyak, Enrique Ramírez de Arellano, Algebras of Toeplitz operators with oscillating symbols. Rev. Mat. Iberoam. 20 (2004), no. 3, pp. 647–671

DOI 10.4171/RMI/404