Folner Conditions, Nuclearity, and Subexponential Growth inC*-Algebras

✍ Scribed by Ghislain Vaillant

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 645 KB
• Volume: 141
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.0136

✦ Synopsis

showed that subexponential growth implies nuclearity in the C*-context. Voiculescu suggested a Fo% lner type condition for C*-algebras and asked about the relation to growth and nuclearity. In this work we clarify the relation among subexponential growth phenomena, this Fo% lner condition suggested by Voiculescu, weak filtrability in the sense of Arveson and Bedos, and nuclearity in the C*-algebra context. 1996 Academic Press, Inc.

MOTIVATION

The work of Gromov and Connes on discrete groups, growth, and Fredholm modules has inspired Voiculescu to initiate a research program on the structure of C*-algebras along the lines of the analoguous study of discrete groups. In particular, Voiculescu pointed out the naturality of the concept of filtration in a C*-algebra, filtrations which play an essential role in the study of C*-growth and Folner type conditions for C*-algebras and their relations to nuclearity.

Answering a first question of Voiculescu [24, Problem 5.9], we showed with Kirchberg that in the C*-context subexponential growth implies nuclearity [19, Corollary 2.2]: if a unital C*-algebra A admits a filtration (

then A is a nuclear C*-algebra.