Module maps over locally compact quantum groups

Zhiguo Hu, Matthias Neufang, and Zhong-Jin Ruan. "Module maps over locally compact quantum groups." Studia Mathematica 211.2 (2012): 111-145. <http://eudml.org/doc/285616>.

@article{ZhiguoHu2012,
abstract = {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 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.},
author = {Zhiguo Hu, Matthias Neufang, Zhong-Jin Ruan},
journal = {Studia Mathematica},
keywords = {locally compact quantum groups; associated Banach algebras; module maps},
language = {eng},
number = {2},
pages = {111-145},
title = {Module maps over locally compact quantum groups},
url = {http://eudml.org/doc/285616},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Zhiguo Hu
AU - Matthias Neufang
AU - Zhong-Jin Ruan
TI - Module maps over locally compact quantum groups
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 2
SP - 111
EP - 145
AB - 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 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.
LA - eng
KW - locally compact quantum groups; associated Banach algebras; module maps
UR - http://eudml.org/doc/285616
ER -