Module maps over locally compact quantum groups

• Autorzy: Zhiguo Hu , Matthias Neufang , Zhong-Jin Ruan
• Języki publikacji: 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.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 22D15: Group algebras of locally compact groups
• 46H05: General theory of topological algebras
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 211
• Numer: 2
• Strony: 111-145

Daty

wydano

2012

Twórcy

autor

Zhiguo Hu

• Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4

autor

Matthias Neufang

• 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

Zhong-Jin Ruan

• Department of Mathematics, University of Illinois, Urbana, IL 61801, U.S.A.

Identyfikatory

DOI

10.4064/sm211-2-2