We are concerned in this paper with the pseudo almost automorphy of mild solutions for the semilinear evolution equation $x'(t)=Ax(t)+f(t,x)$ where $A$ is a sectorial operator not necessarily densely defined in $X$ generating an hyperbolic semigroup $(T(t))_{t\geq 0}$ in a Banach space $X$ and $f:\R\times X_\alpha \to X$, where $X_{\alpha}$ is an intermediate space. We prove the existence and uniqueness of a pseudo almost automorphic solution in $X_\alpha$, when the function $f:\R\times X_\alpha\longrightarrow X$ is pseudo almost automorphic.