Spaces of representations and enveloping l.m.c. ^∗-algebras

Maria Fragoulopoulou

Vol. 95 (1981), No. 1, 61–73

DOI: 10.2140/pjm.1981.95.61

Abstract

Given a l.m.c. ^∗-algebra E with a b.a.i., the space of representations ℛ(E) and the enveloping algebra ℰ(E) of E are defined. Under a suitable condition for the extreme points of E, ℛ(E), ℛ(ℰ(E)) coincide topologically, a fact contributing to the openess of the map defining the topology of ℛ(E). Furthermore, one gets ℰ(E) = ℰ(E_α), within a topological algebraic isomorphism, where (E_α) is the inverse system of Banach algebras corresponding to E.

Mathematical Subject Classification 2000

Primary: 46K10

Secondary: 47D40

Milestones

Received: 18 April 1979

Revised: 24 October 1980

Published: 1 July 1981