On stabilities of functional envelopes and its applications

Abstract

Let (X, f) be a dynamical system and (S(X), F(f)) its functional envelope, where f is continuous. We prove the stabilities of the functional envelope F(f) : S(U)(X) -> S(U)(X) defined by F(f)(g) = f o g; for any g is an element of S(U)(X). And we also obtain some results for the derivations of function spaces.