The weak compactification of locally compact groups
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The weak compactification of locally compact groupsData de publicació
2021Editor
ElsevierISSN
0166-8641Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/acceptedVersionParaules clau / Matèries
Resum
We further investigate the weak topology generated by the irreducible unitary representations of a group G. A deep result due to Ernest [13] and Hughes [22] asserts that every weakly compact subset of a locally compact ... [+]
We further investigate the weak topology generated by the irreducible unitary representations of a group G. A deep result due to Ernest [13] and Hughes [22] 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 [19] 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 countable compactness, pseudocompactness and functional boundedness. [-]
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info:eu-repo/semantics/openAccess
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