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Paper IPM / M / 18008 | ||||||||||||
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Abstract: | ||||||||||||
Let G be a locally compact quantum group. We study the existence of certain (weakly) compact right and left multipliers of the Banach algebra X∗, where X is an introverted subspace of L∞(G) with some conditions, and relate them with some properties of G such as compactness and amenability.For example, when G is co-amenable and L1(G) is semisimple we give a characterization for compactness of G in terms of the existence of a non-zero compact right multiplier on X∗. Using this, for a locally compact group G we prove that Ga is compact if and only if there is a non-zero (weakly) compact right multiplier on X∗. Similar assertion holds for Gs when G is amenable.
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