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Characterising weakly almost periodic functionals on the measure algebra

Matthew Daws (2011)

Studia Mathematica

Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say K W A P . In this paper, we investigate properties of K W A P . We present a short proof that K W A P can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens products. This...

Characterizations of amenable representations of compact groups

Michael Yin-Hei Cheng (2012)

Studia Mathematica

Let G be a locally compact group and let π be a unitary representation. We study amenability and H-amenability of π in terms of the weak closure of (π ⊗ π)(G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.

Characterizing Sidon sets by interpolation properties of subsets

Colin C. Graham, Kathryn E. Hare (2008)

Colloquium Mathematicae

Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups containing...

Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations

Michel Talagrand (1982)

Annales de l'institut Fourier

Let G be a locally compact group. Let L t be the left translation in L ∞ ( G ) , given by L t f ( x ) = f ( t x ) . We characterize (undre a mild set-theoretical hypothesis) the functions f ∈ L ∞ ( G ) such that the map t → L t f from G into L ∞ ( G ) is scalarly measurable (i.e. for φ ∈ L ∞ ( G ) * , t → φ ( L t f ) is measurable). We show that it is the case when t → θ ( L f t ) is measurable for each character θ , and if G is compact, if and only if f is Riemann-measurable. We show that t → L t f is Borel measurable if and only if f is left uniformly continuous.Some of the measure-theoretic tools used there...

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