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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Operator Semigroup Compactifications


Author: H. D. Junghenn
Journal: Trans. Amer. Math. Soc. 348 (1996), 1051-1073
MSC (1991): Primary 22A20, 22A25, 43A60
DOI: https://doi.org/10.1090/S0002-9947-96-01607-8
MathSciNet review: 1348864
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Abstract: A weakly continuous, equicontinuous representation of a semitopological semigroup $S$ on a locally convex topological vector space $X$ gives rise to a family of operator semigroup compactifications of $S$, one for each invariant subspace of $X$. We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.


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Additional Information

H. D. Junghenn
Affiliation: Department of Mathematics, The George Washington University, Washington, D.C. 20052
Email: hugo@math.gwu.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01607-8
Keywords: Semitopological semigroup, left topological compactification, representation, projective limit, inductive limit, tensor product, weakly almost periodic
Received by editor(s): October 27, 1994
Article copyright: © Copyright 1996 American Mathematical Society

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