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Paper   IPM / M / 18008
School of Mathematics
  Title:   Weakly comopact multipliers for some quantum group algebras
  Author(s):  Mehdi Nemati (Joint with R. Esmailvandi and A. Ebrahimzadeh)
  Status:   To Appear
  Journal: Annal. Math.
  Supported by:  IPM
  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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