Small eigenvalue variation and real rank zero
A necessary and sufficient condition, in terms of asymptotic properties of the sequence, is given for the inductive limit of a sequence of finite direct sums of matrix algebras over commutative \(C^*\)-algebras to have real rank zero (i.e., for each selfadjoint element to be approximable by one with finite spectrum).
inductive limit of a sequence of finite direct sums of matrix algebras over commutative \(C^*\)-algebras
scientific article; zbMATH DE number 950177