Abstract
We study nuclearity of the $C^*$-algebra $\mathbb B(\mathcal E)$ of adjointable operators on a full Hilbert $C^*$-module $\mathcal E$ over a $C^*$-algebra $\mathcal A$. When $\mathcal A$ is a von Neumann algebra and $\mathcal E$ is full and self dual, we show that $\mathbb B(\mathcal E)$ is nuclear if and only if $\mathcal A$ is nuclear and $\mathcal E$ is finitely generated. In particular, when $\mathcal A$ is a factor, then nuclearity of $\mathbb B(\mathcal E)$ implies that $\mathcal E$, $\mathcal A$ and $\mathbb B(\mathcal E)$ are finite dimensional.
Citation
Massoud Amini. Mohammad B. Asadi. "On nuclearity of the algebra of adjointable operators." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 423 - 427, august 2015. https://doi.org/10.36045/bbms/1442364589
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