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The dual quasisemigroup and controllability of evolution equations

Abstract:

We study the notion of dual quasisemigroups of bounded linear operators as a generalization of that for strongly continuous semigroup and prove some properties similar to the dual of a semigroup, among other things we prove that for reflexive Banach spaces the dual quasisemigroup is strongly continuous on ( 0, + ∞ ). This allows us to extend some recent criteria of controllability to a general class of evolution equations in reflexive Banach spaces. © 2005 Elsevier Inc. All rights reserved.