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• # Artykuł - szczegóły

## Studia Mathematica

2012 | 211 | 2 | 111-145

## Module maps over locally compact quantum groups

EN

### Abstrakty

EN
We study locally compact quantum groups 𝔾 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 $L_{∞}(𝔾)$ are used to characterize strong Arens irregularity of L₁(𝔾) and are linked to commutation relations over 𝔾 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.

111-145

wydano
2012

### Twórcy

autor
• Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4
autor
• School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
• Université Lille 1 - Sciences et Technologies, UFR de Mathématiques, Laboratoire de Mathématiques Paul Painlevé, UMR CNRS 8524 59655 Villeneuve d'Ascq Cédex, France
autor
• Department of Mathematics, University of Illinois, Urbana, IL 61801, U.S.A.