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Module maps over locally compact quantum groups

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Hu Z., Neufang M., Ruan Z.-J.

Studia Mathematica

2012

tom 211

nr 2

111-145

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.

Ograniczanie wyników

1 Studia Mathematica

1 Hu Z.

1 Neufang M.

1 Ruan Z.-J.

1 2012

Wyniki wyszukiwania

Module maps over locally compact quantum groups