Topological *-algebras with C*-enveloping algebras II

Bhatt, S. J. (2001) Topological *-algebras with C*-enveloping algebras II Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 111 (1). pp. 65-94. ISSN 0253-4142

PDF - Publisher Version

Official URL:

Related URL:


Universal C*-algebras C*(A) exist for certain topological *-algebras called algebras with a C*-enveloping algebra. A Frechet *-algebraA has a C*-enveloping algebra if and only if every operator representation of A maps A into bounded operators. This is proved by showing that every unbounded operator representation Λ, continuous in the uniform topology, of a topological *-algebra A, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through the enveloping pro-C*-algebra E(A) of A. Given a C*-dynamical system (G,A,α), any topological *-algebra B containing Cc (G,A) as a dense C*-subalgebra and contained in the crossed product C*-algebra C*(G,A,α) satisfies E(B) =C*(G,A,α;). If G = R, if B is an α;-invariant dense Frechet *-subalgebra of A such that E(B) =A, and if the action α; on B is m-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS (R,B,α;) satisfies E(S(R,B,α;)) =C*(R,A,α;). WhenG is a Lie group, the C-elements C(A), the analytic elements Cω(A) as well as the entire analytic elements C(A) carry natural topologies making them algebras with a C*-enveloping algebra. Given a non-unital C*-algebra A, an inductive system of ideals Iα; is constructed satisfying A =C*-ind lim Iα;; and the locally convex inductive limit ind lim Iα; is an m-convex algebra with the C*-enveloping algebra A and containing the Pedersen ideal K A of A. Given generators G with weakly Banach admissible relations R, we construct universal topological*-algebra A(G, R) and show that it has a C*-enveloping algebra if and only if (G, R) is C*-admissible.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Frechet *-algebra; Topological *-algebra; C*-enveloping Algebra; Unbounded Operator Representation; O*-algebra ;smooth Frechet Algebra Crossed Product; Pedersen Ideal of a C*-algebra; Groupoidc-algebra; Universal Algebra on Generators with Relations
ID Code:59681
Deposited On:07 Sep 2011 05:17
Last Modified:18 May 2016 10:09

Repository Staff Only: item control page