Filling families and strong pure infiniteness

الأصل · EN

We introduce filling families with matrix diagonalization as a refinement of the work by Rørdam 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 AφN by an endomorphism φ 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 O∞ tensorially.