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Compact and Weakly Compact Multipliers of Locally Compact Quantum Groups

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Abstract

A locally compact group G is compact if and only if its convolution algebra has a non-zero (weakly) compact multiplier. Dually, G is discrete if and only if its Fourier algebra has a non-zero (weakly) compact multiplier. In addition, G is compact (respectively, amenable) if and only if the second dual of its convolution algebra equipped with the first Arens product has a non-zero (weakly) compact left (respectively, right) multiplier. We prove the non-commutative versions of these results in the case of locally compact quantum groups.

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  1. Department of Mathematics, Kharazmi University (Tarbiat Moallem University), 50, Taleghani Ave., Tehran, 15618, Iran

    Alireza Medghalchi & Ahmad Mollakhalili

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  1. Alireza Medghalchi
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  2. Ahmad Mollakhalili
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Correspondence to Ahmad Mollakhalili.

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Communicated by Massoud Amini.

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Medghalchi, A., Mollakhalili, A. Compact and Weakly Compact Multipliers of Locally Compact Quantum Groups. Bull. Iran. Math. Soc. 44, 101–136 (2018). https://doi.org/10.1007/s41980-018-0008-y

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