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This article is devoted to the existence and uniqueness of pathwise solutionsto stochastic evolution equations, driven by a H\"older continuous functionwith H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise.As a particular situation, we shall consider the case where the equation isdriven by a fractional Brownian motion $B^H$ with Hurst parameter $H>1/2$. Incontrast to the article by Maslowski and Nualart, we present here an existenceand uniqueness result in the space of H\"older continuous functions with valuesin a Hilbert space $V$. If the initial condition is in the latter space thisforces us to consider solutions in a different space, which is a generalizationof the H\"older continuous functions. That space of functions is appropriate tointroduce a non-autonomous dynamical system generated by the correspondingsolution 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 dynamicalsystem, defined over the ergodic metric dynamical system generated by theinfinite dimensional fractional Brownian motion

Pathwise solutions of SPDEs driven by H\"older-continuous integrators with exponent larger than 1/2 and random dynamical systems