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Invariant \({\varphi}\)-means on left introverted subspaces with application to locally compact quantum groups

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Abstract

Given a Banach algebra \({{\mathcal{A}}}\), for a non-zero character \({\varphi}\) on \({{\mathcal{A}}}\), we characterize the existence of \({\varphi}\)-means on a left introverted subspace of \({{\mathcal{A}^{*}}}\) containing \({\varphi}\) in terms of certain derivations from \({{\mathcal{A}}}\) into certain Banach \({{\mathcal{A}}}\)-bimodules. We also adapt and extend a result in (Crann and Neufang, Trans Amer Math Soc 368:495–513, 2016) on locally compact quantum groups to the Banach algebra setting which, in particular, answers a question of Bédos and Tuset, concerning the amenability of locally compact quantum groups.

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  1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Mehdi Nemati

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  1. Mehdi Nemati
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Nemati, M. Invariant \({\varphi}\)-means on left introverted subspaces with application to locally compact quantum groups. Arch. Math. 106, 543–552 (2016). https://doi.org/10.1007/s00013-016-0900-8

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