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 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 version of the theorems by Young (1973), Lau (1981), and Forrest (1991) regarding Arens regularity of the group algebra L₁(G) and the Fourier algebra A(G). We extend the classical Eberlein theorem on the inclusion B(G) ⊆ WAP(G) to all locally compact quantum groups.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-2-2,
author = {Zhiguo Hu and Matthias Neufang and Zhong-Jin Ruan},
title = {Module maps over locally compact quantum groups},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {111-145},
zbl = {1269.22004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-2-2}
}
Zhiguo Hu; Matthias Neufang; Zhong-Jin Ruan. Module maps over locally compact quantum groups. Studia Mathematica, Tome 209 (2012) pp. 111-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-2-2/