Electron. J. Diff. Eqns. Vol. 1993(1993), No. 01, pp. 1-7.

Lie Generators for Semigroups of Transformations on a Polish Space

J. R. Dorroh
John W. Neuberger

Let X be a separable complete metric space. We characterize completely the infinitesimal generators of semigroups of linear transformations in Cb(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, Cb(X) is equipped with a locally convex topology known as the strict topology.

Submitted May 8, 1993. Published August 27, 1993.
Math Subject Classification: 47H20, 47D20.
Key Words: semigroups of operators, infinitesimal generator.

An addendum was attached on November 17, 1994. See last page of this article.

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  J. R. Dorroh
Department of Mathematics, Louisiana State University
Baton Rouge, LA 70803, USA
e-mail: mmdorr@lsuvax.sncc.lsu.edu
John W. Neuberger
Department of Mathematics, University of North Texas
Denton, TX 76203, USA
e-mail: jwn@unt.edu

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