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august 2015 On nuclearity of the algebra of adjointable operators
Massoud Amini, Mohammad B. Asadi
Bull. Belg. Math. Soc. Simon Stevin 22(3): 423-427 (august 2015). DOI: 10.36045/bbms/1442364589

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.

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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

Information

Published: august 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1334.46042
MathSciNet: MR3396993
Digital Object Identifier: 10.36045/bbms/1442364589

Subjects:
Primary: 18D05 , 46L55

Keywords: Hilbert $C^*$-modules , Morita equivalence , nuclearity

Rights: Copyright © 2015 The Belgian Mathematical Society

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Vol.22 • No. 3 • august 2015
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