# 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} }

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…

## 4 Citations

### Reproducing kernel Hilbert algebras on compact Lie groups

- Mathematics
- 2019

We describe the construction of a nested family of Hilbert spaces $\{ \mathcal{H}_\tau : \tau>0 \}$ of functions on a torus, which also have a $C^*$ algebra structure under the pointwise product of…

### An $H^p$ scale for complete Pick spaces

- MathematicsStudia Mathematica
- 2021

We define by interpolation a scale analogous to the Hardy $H^p$ scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call $\mathcal{H}^p$. In…

### On the column-row property of Operator spaces

- Mathematics
- 2022

. 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…

### Every complete Pick space satisfies the column-row property

- Mathematics
- 2020

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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