CHARACTERIZATION OF CONTINUOUS FUNCTIONS ON OPEN CONNECTED SUBSET OF

Fatima M. Azmi (Saudi Arbia)

Received February 7, 2007; Revised April 25, 2007

Abstract

Let A be a Fréchet * -algebra with n-pairwise commuting self-adjoint generators and with no nontrivial idempotent. By imposing the condition that the joint spectral image of the generators contains no boundary points, we are led to a definition of n-special algebra, and prove that the character of A is homeomorphic to an open connected subset of Then by adopting a suitable generalization of the Gelfand-Naimark theorem, we characterize the algebra of all continuous complex valued functions defined on open connected subset of

Keywords and phrases: C ^* algebra, Fréchet * -algebra, Gelfand Naimark theorem, character of A, joint spectrum.