TY - JOUR
AU - Hadwin, Don
PY - 2014/08/12
Y2 - 2024/05/29
TI - A Lifting Characterization of Rfd C*-Algebras
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 115
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-18004
UR - https://www.mscand.dk/article/view/18004
SP - 85-95
AB - We prove a conjecture of Terry Loring that characterizes separable RFD C*-algebras in terms of a lifting property. In addition we introduce and study generalizations of RFD algebras. If $k$ is an infinite cardinal, we say a C*-algebra is residually less than $k$ dimensional, if the family of representations on Hilbert spaces of dimension less than $k$ separates the points of the algebra. We give characterizations of this property and prove that this class is closed under free products in the nonunital category. For free products in the unital category, the results depend on the cardinal $k$.
ER -