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arXiv · 2001.07051

Herz-Schur Multipliers of Fell Bundles

Weijiao He
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Abstract

In this paper we develop the notion of Herz-Schur multipliers to the context of Fell bundle, and we give a necessary and sufficient condition if the reduced cross-sectional $C^{\ast}$-algebra $C_r^{\ast}(\mathfrak{B})$ of Fell bundle $\mathfrak{B}$ over discrete group $G$ is nuclear in terms of this generalized notion. As an application, we prove that if $C_r^{\ast}(\mathfrak{B})$ is nuclear, then for any subgroup $H \subset G$, the $C^{\ast}$-algebra $C_r^{\ast}(\mathfrak{B}_H)$ is nuclear.

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Weijiao He. 2020-01-20. Herz-Schur Multipliers of Fell Bundles. https://arxiv.org/abs/2001.07051

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