Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces

In this paper, we prove that the space (PAA( R, X), parallel to center dot parallel to(0)) is complete. This not only gives an affirmative answer to a basic problem in this field, but also enables us to obtain an existence and uniqueness theorem of pseudo almost automorphic mild solutions to semilinear differential equations in Banach spaces. An example is given to illustrate our theorem.