A Hille-Yosida theorem for Bi-continuous semigroups |
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Authors: | Email author" target="_blank">Franziska?KuhnemundEmail author |
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Institution: | (1) Mathematisches Institut, Universitat Tubingen, Auf der Morgenstelle 10 D–72076 Tubingen, Germany |
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Abstract: | In order to treat one-parameter semigroups of linear operators on Banach spaces which are not strongly continuous, we introduce the concept of bi-continuous semigroups defined on Banach spaces with an additional locally convex topology . On such spaces we define bi-continuous semigroups as semigroups consisting of bounded linear operators which are locally bi-equicontinuous for and such that the orbit maps are -continuous. We then apply the result to semigroups induced by flows on a metric space as studied by J. R. Dorroh and J. W. Neuberger. |
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