Filling families and strong pure infiniteness

Eberhard Kirchberg; Adam Sierakowski

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arXiv · 1503.08519

Filling families and strong pure infiniteness

Eberhard Kirchberg·Adam Sierakowski

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Abstract

We introduce filling families with matrix diagonalization as a refinement of the work by R{\o}rdam and the first named author. As an application we improve a result on local pure infiniteness and show that the minimal tensor product of a strongly purely infinite $C^*$-algebra and a exact $C^*$-algebra is again strongly purely infinite. Our results also yield a sufficient criterion for the strong pure infiniteness of crossed products $A\rtimes_\varphi \mathbb{N}$ by an endomorphism $\varphi$ of $A$ (cf. Theorem 7.6). Our work confirms that the special class of nuclear Cuntz-Pimsner algebras constructed by Harnisch and the first named author consist of strongly purely infinite $C^*$-algebras, and thus absorb $\mathcal{O}_\infty$ tensorially.

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Eberhard Kirchberg, Adam Sierakowski. 2015-03-30. Filling families and strong pure infiniteness. https://arxiv.org/abs/1503.08519

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