ON THE CONTINUITY OF THE ADJOINT OF EVOLUTION OPERATORS

Abstract

By associating a quasi semigroup to a commutative evolution operator and using techniques from vector measures like the Gel?fand integral and the Radon-Nikodym theorem for Bochner integral, we prove the continuity on [0, ?) of the adjoint of a certain class of evolution operators. Furthermore, we provide examples of evolution operators satisfying our conclusion. We also provide an application to optimal control theory; particularly, to an optimal control problem governed by a time-varying heat equation

Keywords

Gel?fand integral, adjoint of evolution operators, Asplund spaces, strongly continuous semigroups

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