FOLNER CONDITIONS, NUCLEARITY, AND SUBEXPONENTIAL GROWTH IN C-ASTERISK-ALGEBRAS

Answering a first question of Voiculescu (On the existence of quasi-ce ntral approximate units relative to normed ideals, J. Funct. Anal. 91 (1990); 1-36) Vaillant and Kirchberg (On C-algebras having subexponen tial, polynomial and linear growth, Invent. Math. 108 (1992), 635-652) showed that subexponential growth implies nuclearity in the C-contex t. Voiculescu suggested a Folner type condition For C-algebras and as ked about the relation to growth and nuclearity. in this work we clari fy the relation among subexponential growth phenomenal this Folner con dition suggested by Voiculescu, weak filtrability in the sense of Arve son and Bedos, and nuclearity in the C-algebra context. (C) 1996 Acad emic Press, Inc.