Controllability of linear systems in Banach spaces

The problem of controllability of linear systems in Banach spaces is considered. First, some properties of dual semigroups with respect to Lebesgue measure is presented. Then, based on the properties, the criteria for controllability in reflexive Banach spaces are extended to general Banach spaces and some new criteria for controllability are established. An example is presented to show that the scope of controllable systems can be enlarged if the non-traditional space of control functions is used. (C) 2002 Elsevier Science B.V. All rights reserved.