Helson operators and coinvariant subspaces
Volume 270 / 2023
Studia Mathematica 270 (2023), 209-228
MSC: Primary 47A15; Secondary 47B35, 30H20.
DOI: 10.4064/sm220407-19-9
Published online: 26 October 2022
Abstract
We give an explicit expression of the functions in the finite-dimensional coinvariant subspace of the Hardy and weighted Bergman spaces over the infinite polydisc. As an application, an alternative form of the Perfekt–Pushnitski theorem characterizing Helson operators with finite rank is obtained. Interestingly, it turns out that a Helson operator is automatically bounded if it is of finite rank.
