J. R. Dorroh
John W. Neuberger
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 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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