Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590628 | Journal of Functional Analysis | 2013 | 22 Pages |
Abstract
We prove two versions of Bochnerʼs theorem for locally compact quantum groups. First, every completely positive definite “function” on a locally compact quantum group G arises as a transform of a positive functional on the universal C⁎-algebra of the dual quantum group. Second, when G is coamenable, complete positive definiteness may be replaced with the weaker notion of positive definiteness, which models the classical notion. A counterexample is given to show that the latter result is not true in general. To prove these results, we show two auxiliary results of independent interest: products are linearly dense in , and when G is coamenable, the Banach ⁎-algebra has a contractive bounded approximate identity.
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