JournalszaaVol. 28 , No. 1DOI 10.4171/zaa/1376

Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range

  • L. P. Castro

    Universidade de Aveiro, Portugal
  • A. S. Silva

    Universidade de Aveiro, Portugal
Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range cover

Abstract

We characterize left, right and both-sided invertibility of matrix Wiener--Hopf plus Hankel operators with possibly different Fourier symbols in the Wiener subclass of the almost periodic algebra. This is done when a certain almost periodic matrix-valued function (constructed from the initial Fourier symbols of the Hankel and Wiener–Hopf operators) admits a numerical range bounded away from zero. The invertibility characterization is based on the value of a certain mean motion. At the end, an example of a concrete Wiener–Hopf plus Hankel operator is studied in view of the illustration of the proposed theory.