On the Norm Continuity of ^'-valued Gaussian Processes

Let Sf be the Schwartz space of all rapidly decreasing functions on R, Sf be the topological dual space of Sf and for each positive integer p,Sfp be the space of all elements of £f' which are continuous in the p-th norm defining the nuclear Frechet topology of Sf. The main purpose of the present paper is to show that if {Xtί t e [0, + oo)} is an ^'-valued Gaussian process and for any fixed φβ^ the real Gaussian process {Xt(φ)91 e [0, + oo)} has a continuous version, then for any fixed T > 0 there is a positive integer p such that {Xt, t e [0, T]} has a version which is continuous in the norm topology of S?'p.