Module maps over locally compact quantum groups

作者：Hu Zhiguo^*; Neufang Matthias; Ruan Zhong Jin

来源：Studia Mathematica, 2012, 211(2): 111-145.

DOI：10.4064/sm211-2-2

• locally compact quantum groups and associated Banach algebras
• module maps

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 L-1 (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 L-1 (G) and the Fourier algebra A(G). We extend the classical Eberlein theorem on the inclusion B(G) subset of WAP(G) to all locally compact quantum groups.

• 出版日期2012