The weak compactification of locally compact groups
arXiv (Cornell University)(2021)
摘要
We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally compact (LC) group $G$ is compact in the LC-topology, generalizing thereby a previous result of Glicksberg \cite{glicks1962} for abelian locally compact (LCA) groups. Here, we first survey some recent findings on the weak topology and establish some new results about the preservation of several compact-like properties when going from the weak topology to the original topology of LC groups. Among others, we deal with the preservation of countably compactness, pseudocompactness and functional boundedness.
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关键词
weak compactification,compactification groups
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