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Generalized Calderón conditions and regular orbit spaces

Hartmut Führ (2010)

Colloquium Mathematicae

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L²(A) requires the existence of a square-integrable function whose Plancherel transform satisfies a Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable functions exist. The existing literature on this subject leaves a gap between sufficient and necessary criteria....

Group C*-algebras satisfying Kadison's conjecture

Rachid El Harti, Paulo R. Pinto (2011)

Banach Center Publications

We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that A ⊗ m i n B inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove that G/Γ is...

Growth functions for some uniformly amenable groups

Janusz Dronka, Bronislaw Wajnryb, Paweł Witowicz, Kamil Orzechowski (2017)

Open Mathematics

We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.

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