This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form where belongs to some algebra of functions on the unit circle and 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.
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Albrecht Böttcher, Alexander Poznyak, Enrique Ramírez de Arellano, Algebras of Toeplitz operators with oscillating symbols. Rev. Mat. Iberoam. 20 (2004), no. 3, pp. 647–671DOI 10.4171/RMI/404