An Invertibility Criterion in a C*-Algebra Acting on the Hardy Space with Applications to Composition Operators


GÜL U. , Koca B. B.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.15, no.6, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.1007/s00009-018-1268-8
  • Title of Journal : MEDITERRANEAN JOURNAL OF MATHEMATICS

Abstract

In this paper, we prove an invertibility criterion for certain operators which is given as a linear algebraic combination of Toeplitz operators and Fourier multipliers acting on the Hardy space of the unit disc. Very similar to the case of Toeplitz operators, we prove that such operators are invertible if and only if they are Fredholm and their Fredholm index is zero. As an application, we prove that for quasi-parabolic composition operators the spectra and the essential spectra are equal.