Portugaliae Mathematica


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Volume 66, Issue 2, 2009, pp. 147–158
DOI: 10.4171/PM/1837

Published online: 2009-06-30

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

Romeo Meštrović[1] and Žarko Pavićević

(1) University of Montenegro, Kotor, Montenegro

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 Np, 1 < p < ∞, in a certain topology. For a fixed p we define the class Hp consisting of those de Branges spaces ℋ(b) such that the function b is not an extreme point of the unit ball of H, and the associated measure μb for b satisfies an additional condition. It is proved that the function f analytic on D is a multiplier of every de Branges space from Hp if and only if f is in the intersection of the ranges of all Toeplitz operators belonging to the class Hp. We show that this is true if and only if the Taylor coefficients \hat{f}(n) of f decay like O(exp (−cn1/(p + 1))) for a positive constant c.

Keywords: Toeplitz operator, Privalov class Np, Helson topology, weight, de Branges space, multipliers

Meštrović Romeo, Pavićević Žarko: A note on common range of a class of co-analytic Toeplitz operators. Port. Math. 66 (2009), 147-158. doi: 10.4171/PM/1837