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This paper studies the notions of controllability for the linear sys- tems associated with the generator of an exponentially bounded C-semigroup in a Banach space, controls also belonging to Banach spaces. Necessary and sufficient conditions are obtained in that framework, and the duality property is studied, which generalize the corresponding results of the linear systems as- sociated with the generator of a strongly continuous semigroup.

Controllability of a class of linear systems in Banach space