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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 4, Pages 195-207
http://dx.doi.org/10.1155/S0161171202011559

On the extensions of infinite-dimensional representations of Lie semigroups

Department of Mathematics, Gomel State University, Sovietskaya, 104, Gomel 246699, Belarus

Received 22 January 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The necessary and sufficient conditions have been obtained for extendability of a Banach representation of a generating Lie semigroup S to a local representation of the Lie group G generated by S when the tangent wedge of S is a Lie semialgebra. The most convenient conditions we obtain correspond to the case of unitary representations. In this case, we give a criterion of global extendability if G is exponential and solvable.