Page 1 Next

Displaying 1 – 20 of 24

Showing per page

Metrization criteria for compact groups in terms of their dense subgroups

Dikran Dikranjan, Dmitri Shakhmatov (2013)

Fundamenta Mathematicae

According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or G δ -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...

Module maps over locally compact quantum groups

Zhiguo Hu, Matthias Neufang, Zhong-Jin Ruan (2012)

Studia Mathematica

We study locally compact quantum groups and their module maps through a general Banach algebra approach. As applications, we obtain various characterizations of compactness and discreteness, which in particular generalize a result by Lau (1978) and recover another one by Runde (2008). Properties of module maps on L ( ) are used to characterize strong Arens irregularity of L₁() and are linked to commutation relations over with several double commutant theorems established. We prove the quantum group...

Currently displaying 1 – 20 of 24

Page 1 Next