Characterization of Separable Operator Algebras
by
Paul Haworth
Lancaster University

The approximately finite (AF) C^*-algebras are completely characterized by the local description that any finite family of elements almost lies in a finite dimensional C^*-subalgebra. This was proved first by Glimm for the unital UHF algebras and later extended by Dixmier. More recently, Heffernan generalised these results to nonselfadjoint contexts and demonstrated the uniformly T₂-algebras (limits of nest algebras with self adjoint part M_n1\oplusM_n2) to be similarly locally approximable. This talk will be concerned with extending this intrinsic characterization to cover the AF nest algebras of bounded diameter, or, in keeping with the above terminology, the uniformly T_r-algebras, for arbitrary fixed r.

Later, we shall focus attention on those algebras arising as the dense union of a chain of digraph algebras each regularly embedded in the next. In this setting we provide a new local description which captures the assumed regularity of the system. More importantly however, we will be able to dispense with the bounded diameter constraint imposed above and characterize limits from a much wider class of algebras than previously.

Date received: April 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacw-47.