Small eigenvalue variation and real rank zero

Ola Bratteli and George A. Elliott

Vol. 175 (1996), No. 1, 47–59

DOI: 10.2140/pjm.1996.175.47

Abstract

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 self-adjoint element to be approximible by one with finite spectrum).

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 5 January 1994

Published: 1 September 1996