Boundedness, compactness and Schatten class for Rhaly matrices

Abstract

In this article we present new proofs for the boundedness and the compactness on ${\ell }^2$ of the Rhaly matrices, also known as terraced matrices. We completely characterize when such matrices belong to the Schatten class ${\mathcal{S}}^q({\ell }^2)$, for $1<q<\infty$. Finally, we apply our results to study the Hadamard multipliers in weighted Dirichlet spaces, answering a question left open by Mashreghi-Ransford.