PROJECTIVE LIMIT OF A SEQUENCE OF BANACH FUNCTION ALGEBRAS AS A FRECHET FUNCTION ALGEBRA

Let X be a hemicompact space with () as an admissible exhaustion, and for each n N, a Banach function algebra on with respect to such that and for all f, We consider the subalgebra A = { f C(X) : of C(X) as a frechet function algebra and give a result related to its spectrum when each is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.