Electronic Journal of Differential Equations Vol. 1993 (1993) No. 01, pp.1-7.
Title: Lie Generators for Semigroups of Transformations on a Polish Space
Authors: J. R. Dorroh (Louisiana State Univ., Baton Rouge, LA, USA)
John W. Neuberger (Univ. of North Texas, Denton, TX, USA)
Abstract: Let $X$ be a separable complete metric space.
We characterize completely the infinitesimal generators of semigroups
of linear transformations in $C_b(X)$, the bounded real-valued
continuous functions on $X$, that are induced by
strongly continuous semigroups of continuous transformations in $X$.
In order to do this, $C_b(X)$ is equipped with a locally convex topology
known as the {\it strict topology. }
Submitted May 8, 1993. Published August 27, 1993.
Math Subject Classification: 47H20, 47D20.
Key Words: Semigroups of operators; infinitesimal generator.
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