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

Answering a first question of Voiculescu (On the existence of quasi-central approximate units relative to normed ideals,J. Funct. Anal.91(1990), 1–36) Vaillant 8?and Kirchberg (OnC*-algebras having subexponential, polynomial and linear growth,Invent. Math.108(1992), 635–652) showed that subexponential growth implies nuclearity in theC*-context. Voiculescu suggested a Følner type condition forC*-algebras and asked about the relation to growth and nuclearity. In this work we clarify the relation among subexponential growth phenomena, this Følner condition suggested by Voiculescu, weak filtrability in the sense of Arveson and Bedos, and nuclearity in theC*-algebra context.