Extension of Fourier algebra homomorphisms to duals of algebras of uniformly continuous functionals

Ilie, Monica; Stokke, Ross

doi:10.1016/j.jfa.2008.10.003

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Definitions and Preliminary Results1

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“…The corollary below follows immediately from Proposition 2.1 and its proof. See [31] for results on extension of reduced Fourier-Stieltjes algebra homomorphisms.…”

Section: Definitions and Preliminary Resultsmentioning

confidence: 99%

Module maps over locally compact quantum groups

Neufang

Ruan

2012

Studia Math.

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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 also extend the classical Eberlein theorem on the inclusion B(G) ⊆ W AP (G) to all locally compact quantum groups.

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“…The corollary below follows immediately from Proposition 2.1 and its proof. See [31] for results on extension of reduced Fourier-Stieltjes algebra homomorphisms.…”

Section: Definitions and Preliminary Resultsmentioning

confidence: 99%