Characterization of continuous functions on open connected subset of Rn¤

Abstract

Let A be a Fr¶echet * algebra with n- pairwise commuting self adjoint generators and with no non trivial idempotent. By imposing the condition that the joint spectral image of the generators contains no boundary points, we are led to a de¯nition of n-special F¤ algebra, and prove that the character M(A) of A is homeomorphic to an open connected subset of Rn. Then by adopting a suitable eneralization of the Gelfand Naimark theorem, we characterize the algebra of all continuous complex valued functions de¯ned on open connected subset of Rn.