Algebras of Toeplitz operators with oscillating symbols

• Autores: Sergei M. Grudsky, Albrecht Böttcher, E Ramírez de Arellano
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 20, Nº 3, 2004, págs. 647-671
• Idioma: inglés
• DOI: 10.4171/rmi/404
• Títulos paralelos:
  • Algebras de operadores de Toeplitz con símbolos oscilantes.
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• Resumen

  • This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a 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.