Interfaces between Noncommutative Ring Theory and Operator Algebras
by
Pere Ara
Universitat Autònoma de Barcelona

I will present a unified approach to several constructions in operator algebras that are related to the algebraic theory of rings of quotients, showing deep relations between algebraic and analytic concepts. These constructions include the algebra of unbounded operators affiliated to a finite von Neumann algebra, defined by Murray and von Neumann in 1936, and the C^*-algebra of essential multipliers of a C^*-algebra, defined by Elliott in 1976. In both cases, the algebras were defined without any explicit reference to localisation theory, but the fact that they can be obtained as quotient algebras has played a very important role in several applications.

Date received: February 24, 2001

Copyright © 2001 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 # cage-09.