A note on common range of a class of co-analytic Toeplitz operators

  • Romeo Meštrović

    University of Montenegro, Kotor, Montenegro
  • Žarko Pavićević

    University of Montenegro, Podgorica, Montenegro

Abstract

We characterize the intersection of the ranges of a class of co-analytic Toeplitz operators by considering this set as the dual space of the Privalov space , , in a certain topology. For a fixed we define the class consisting of those de Branges spaces such that the function is not an extreme point of the unit ball of , and the associated measure for satisfies an additional condition. It is proved that the function analytic on is a multiplier of every de Branges space from if and only if is in the intersection of the ranges of all Toeplitz operators belonging to the class . We show that this is true if and only if the Taylor coefficients of decay like for a positive constant .

Cite this article

Romeo Meštrović, Žarko Pavićević, A note on common range of a class of co-analytic Toeplitz operators. Port. Math. 66 (2009), no. 2, pp. 147–158

DOI 10.4171/PM/1837