# Multipliers and operator space structure of weak product spaces

@article{Clouatre2019MultipliersAO,
title={Multipliers and operator space structure of weak product spaces},
author={Raphael Clouatre and Michael Hartz},
journal={Analysis \& PDE},
year={2019}
}
• Published 27 September 2019
• Mathematics
• Analysis & PDE
In the theory of reproducing kernel Hilbert spaces, weak product spaces generalize the notion of the Hardy space $H^1$. For complete Nevanlinna-Pick spaces $\mathcal H$, we characterize all multipliers of the weak product space $\mathcal H \odot \mathcal H$. In particular, we show that if $\mathcal H$ has the so-called column-row property, then the multipliers of $\mathcal H$ and of $\mathcal H \odot \mathcal H$ coincide. This result applies in particular to the classical Dirichlet space and to…
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. In this article, we study the following question asked by Michael Hartz in a recent paper [Har20]: which operator spaces satisfy the column-row property? We provide a complete classiﬁcation of the
In the theory of complete Pick spaces, the column-row property has appeared in a variety of contexts. We show that it is satisfied by every complete Pick space in the following strong form: each

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