  This article is devoted to the existence and uniqueness of pathwise solutions
to stochastic evolution equations, driven by a H\"older continuous function
with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise.
As a particular situation, we shall consider the case where the equation is
driven by a fractional Brownian motion $B^H$ with Hurst parameter $H>1/2$. In
contrast to the article by Maslowski and Nualart, we present here an existence
and uniqueness result in the space of H\"older continuous functions with values
in a Hilbert space $V$. If the initial condition is in the latter space this
forces us to consider solutions in a different space, which is a generalization
of the H\"older continuous functions. That space of functions is appropriate to
introduce a non-autonomous dynamical system generated by the corresponding
solution to the equation. In fact, when choosing $B^H$ as the driving process,
we shall prove that the dynamical system will turn out to be a random dynamical
system, defined over the ergodic metric dynamical system generated by the
infinite dimensional fractional Brownian motion
