On the lack of exact controllability for mild solutions in Banach spaces

AbstractIt is shown that exact controllability in finite time for linear control systems given on an infinite dimensional separable Banach space in integral form (mild solution) can never arise using locally L1-controls, if the operator through which the control acts on the system is compact. This improves a previous result of the author, by removing the assumption that the state space have a basis. It is suggested by the recent discovery that a separable Banach space need not have a basis