Journal of Operator Theory

Volume 66, Issue 2, Fall 2011 pp. 353-384.

Quasi-diagonal flows

Authors: Akitaka Kishimoto (1) and Derek W. Robinson (2)
Author institution: (1) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
(2) Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia

Summary: We introduce two notions for flows (or one-parameter automorphism groups) on quasi-diagonal $C^*$-algebras, quasi-diagonal and pseudo-diagonal flows; the former being apparently stronger than the latter. We derive basic facts about these flows and give various examples. In addition we extend results of Voiculescu from quasi-diagonal $C^*$-algebras to these flows.

Keywords: $C^*$-algebra, flow, approximately inner, crossed product, KMS state, quasi-diagonal, pseudo-diagonal, Weyl--von Neumann theorem

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