George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4; e-mail: elliott@math.toronto.edu

Mohammad Rouzbehani, School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran; e-mail: rouzbehani.m.math@gmail.com

Abstract/Résumé:

We show that a C*-algebra with topological dimension zero is purely infinite if it is weakly purely infinite (a question of Kirchberg and Rørdam). We give an application of this result.

On démontre qu’une C*-algèbre de dimension topologique égale à zéro est purement infinie si elle est faiblement purement infinie (une question de Kirchberg et de Rørdam). On donne une application de ce résultat.

Keywords: (weak) pure infiniteness, C*-algebra, topological dimension zero

AMS Subject Classification: General theory of $C^*$-algebras 46L05

PDF(click to download): Weakly Purely Infinite C*-algebras with Topological Dimension Zero are Purely Infinite