Operator Semigroup Compactifications

Junghenn, H.

doi:10.1090/S0002-9947-96-01607-8

Operator Semigroup Compactifications
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by H. D. Junghenn

Trans. Amer. Math. Soc. 348 (1996), 1051-1073

DOI: https://doi.org/10.1090/S0002-9947-96-01607-8

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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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