# 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 $N_{p}$, $1<p <∞$, in a certain topology. For a fixed $p$ we define the class $H_{p}$ 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 $μ_{b}$ 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 $H_{p}$ if and only if $f$ is in the intersection of the ranges of all Toeplitz operators belonging to the class $H_{p}$. We show that this is true if and only if the Taylor coefficients $f^ (n)$ of $f$ decay like $O(exp(−cn_{1/(p +1)}))$ for a positive constant $c$.

## 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