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A concavity property for the measure of product sets in groups

Imre Ruzsa (1992)

Fundamenta Mathematicae

Let G be a connected locally compact group with a left invariant Haar measure μ. We prove that the function ξ(x) = inf μ̅(AB): μ(A) = x is concave for any fixed bounded set B ⊂ G. This is used to give a new proof of Kemperman’s inequality μ ̲ ( A B ) m i n ( μ ̲ ( A ) + μ ̲ ( B ) , μ ( G ) ) for unimodular G.

A descriptive view of unitary group representations

Simon Thomas (2015)

Journal of the European Mathematical Society

In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if G and H are countable amenable non-type I groups, then the unitary duals of G and H are Borel isomorphic.

A generalization of amenability and inner amenability of groups

Ali Ghaffari (2012)

Czechoslovak Mathematical Journal

Let G be a locally compact group. We continue our work [A. Ghaffari: Γ -amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of Γ -amenability of a locally compact group G defined with respect to a closed subgroup Γ of G × G . In this paper, among other things, we introduce and study a closed subspace A Γ p ( G ) of L ( Γ ) and then characterize the Γ -amenability of G using A Γ p ( G ) . Various necessary and sufficient conditions are found for a locally compact group to possess...

A generalized notion of n -weak amenability

Abasalt Bodaghi, Behrouz Shojaee (2014)

Mathematica Bohemica

In the current work, a new notion of n -weak amenability of Banach algebras using homomorphisms, namely ( ϕ , ψ ) - n -weak amenability is introduced. Among many other things, some relations between ( ϕ , ψ ) - n -weak amenability of a Banach algebra 𝒜 and M m ( 𝒜 ) , the Banach algebra of m × m matrices with entries from 𝒜 , are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra L 1 ( G ) is ( ϕ , ψ )- n -weakly amenable for any...

A Note on L-sets

Gero Fendler (2002)

Colloquium Mathematicae

Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.

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