Department of Mathematics

Dr. Richard Kraaij, Ruhr-Universität Bochum: "A generation theorem for strongly continuous semigroups on locally convex spaces"

Jun 01, 2017 from 02:00 PM to 03:30 PM

LMS 4 -Raum 526 - Übungsraum

Abstract:  The Hille-Yosida theorem gives necessary and sufficient conditions for an unbounded operator $A$ on a Banach space to generate a strongly continuous semigroup S(t) = exp(tA).

In probability theory(i.e. Markov processes) one finds that natural semigroups are often not strongly continuous for the norm topology on the space of continuous and bounded functions. A similar issue occurs for quantum dynamical semigroups on the space of bounded operators on a Hilbert space. In both settings, there is a natural locally convex topology that is weaker than the norm topology for which the semigroups are strongly continuous.
In the talk, we discuss an extension of the Hille-Yosida theorem to a class of well-behaved locally convex spaces. For the proof we use introduce and use the probabilistic techniques of stochastic domination and concentration inequalities.

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