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Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani, Sima Soltani Renani (2011)

Studia Mathematica

Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Character inner amenability of certain Banach algebras

H. R. Ebrahimi Vishki, A. R. Khoddami (2011)

Colloquium Mathematicae

Character inner amenability for a certain class of Banach algebras including projective tensor products, Lau products and module extensions is investigated. Some illuminating examples are given.

Character pseudo-amenability of Banach algebras

Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.

Character sums in complex half-planes

Sergei V. Konyagin, Vsevolod F. Lev (2004)

Journal de Théorie des Nombres de Bordeaux

Let A be a finite subset of an abelian group G and let P be a closed half-plane of the complex plane, containing zero. We show that (unless A possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of A which belongs to P . In other words, there exists a non-trivial character χ ∈ G ^ such that ∑ a ∈ A χ ( a ) ∈ P .

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...

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