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| Paper IPM / M / 17353 | ||||||||||||||||
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Let G be a locally compact quantum group.Then the space T(L2(G)) of trace class operators on L2(G)
is a Banach algebra with the convolution induced by the right fundamental unitary of G. We show that properties of G such as amenability, triviality and compactness are equivalent to the existence of left or right invariant means on the convolution Banach algebra T(L2(G)). We also investigate the relation between the existence of certain (weakly) compact right and left multipliers of T(L2(G))∗∗ and some properties of G.
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