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Search: MSC category 43A35 ( Positive definite functions on groups, semigroups, etc. )

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1. CJM Online first

Runde, Volker; Viselter, Ami
On positive definiteness over locally compact quantum groups
The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.

Keywords:bicrossed product, locally compact quantum group, non-commutative $L^p$-space, positive-definite function, positive-definite measure, separation property
Categories:20G42, 22D25, 43A35, 46L51, 46L52, 46L89

2. CJM 2008 (vol 60 pp. 1001)

Cornulier, Yves de; Tessera, Romain; Valette, Alain
Isometric Group Actions on Hilbert Spaces: Structure of Orbits
Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.

Keywords:affine actions, Hilbert spaces, minimal actions, nilpotent groups
Categories:22D10, 43A35, 20F69

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