We provide a characterization of when a von Neumann algebra $M$ equipped with a faithful normal semifinite weight $\varphi$ is purely atomic in terms of the existence of certain bounded embeddings of $\mathcal{H}_\varphi$ into $M$ based on a result of Fidaleo and Zsido (2016). We further extend this result to characterize purely atomic von Neumann algebras in terms of the existence of similar bounded embeddings into $M$ of the noncommutative $L^p$-spaces associated to $M$. This is joint work with Panchugopal Bikram and Kunal Krishna Mukherjee. | 
