Abstract
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 L1(G) are used to characterize strong Arens irregularity of L ∞(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) ? WAP(G) to all locally compact quantum groups.
Original language | English (US) |
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Pages (from-to) | 111-145 |
Number of pages | 35 |
Journal | Studia Mathematica |
Volume | 211 |
Issue number | 2 |
DOIs | |
State | Published - 2012 |
Keywords
- Locally compact quantum groups and associated Banach algebras
- Module maps
ASJC Scopus subject areas
- General Mathematics