Controllability of Linear Systems in Non-Reflexive Banch Spaces

Let X and U be Banch spaces, S(t) a C 0 semi group in X , A the infinitesimal generator of S(t) , and B∈L(U,X ). In this paper, we consider the controllability of the system Σ p: (t)=Ax(t)+Bu(t), u∈L p  loc ([0,∞), U), 1≤p<∞. First, we prove that x *∈X *, T, B *S *(t)x * is measurable on [0,T] if X * or U * has Radon Nikodуm property. Then we apply the result to the controllability of the system Σ p and extend the results of controllability in reflexive Banch spaces to non reflexive Banch spaces.