Workshop on Projective Limits and Balanced Topological Groups.
by
G. L. Itzkowitz
Queens College, CUNY.

A "balanced group" is one in which the left and right uniform structures are equivalent and a "functionally balanced group" is one on which the classes of left uniformly continuous bounded real valued functions and those that are right uniformly continuous coincide. In joint work with S.Rothman, H. Strassberg, and T.S. Wu, we used projective limits of Lie groups (often called approximation by Lie groups) to show that the two concepts are equivalent for locally compact groups. This, together with a classical theorem of Graev suggested that this result might be extended to those groups that are projective limits of metric groups.

The workshop notes consist of three sections: Section 1, "Projective limits of topological groups, " presents a quick introduction with proofs to the concept of a projective limit of topological groups. In section 2, "Functionally balanced groups, " we introduce the concept of a functionally balanced group. It describes an important chracterization of such groups and an important corollary of this theorem. Finally, the third section, "Projective limits of groups, " has a complete proof of Graev's motivating theorem and applies these results to obtain a number of theorems, which to my knowledge are new, concerning projective limits of metric groups.

Date received: June 15, 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 # cacl-80.