A characterization of algebraic measures
A characterization of the invertible measures
Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
A characterization of α-convolutions
A generalized notion of -weak amenability
In the current work, a new notion of -weak amenability of Banach algebras using homomorphisms, namely --weak amenability is introduced. Among many other things, some relations between --weak amenability of a Banach algebra and , the Banach algebra of matrices with entries from , 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 is ()--weakly amenable for any...
A note on translates of bounded measures
A positivity result and normalization of positive convolution structures.
Absolut stetige Maße auf lokalkompakten Halbgruppen.
Algèbres de Fourier associées à une algèbre de Kac.
Amenability for dual Banach algebras
We define a Banach algebra 𝔄 to be dual if 𝔄 = (𝔄⁎)* for a closed submodule 𝔄⁎ of 𝔄*. The class of dual Banach algebras includes all W*-algebras, but also all algebras M(G) for locally compact groups G, all algebras ℒ(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions an amenable...
An algebra of finitely additive measures
An analogue in commutative harmonic analysis of the uniform bounded approximation property of Banach space
An analogue of Hardy's theorem for the Heisenberg group
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.
An elementary proof of the decomposition of measures on the circle group
We give an elementary proof for the case of the circle group of the theorem of O. Hatori and E. Sato, which states that every measure on a compact abelian group G can be decomposed into a sum of two measures with a natural spectrum and a discrete measure.
An F. and M. Riesz theorem for compact Lie groups.
An semigroup of zero measure which contains a translate of every countable set
Asymptotisch gleichverteilte Netze von Wahrscheinlichkeitsmassen auf lokalkompakten Gruppen
Banach algebras with unique uniform norm II
Semisimple commutative Banach algebras 𝓐 admitting exactly one uniform norm (not necessarily complete) are investigated. 𝓐 has this Unique Uniform Norm Property iff the completion U(𝓐) of 𝓐 in the spectral radius r(·) has UUNP and, for any non-zero spectral synthesis ideal ℐ of U(𝓐), ℐ ∩ 𝓐 is non-zero. 𝓐 is regular iff U(𝓐) is regular and, for any spectral synthesis ideal ℐ of 𝓐, 𝓐/ℐ has UUNP iff U(𝓐) is regular and for any spectral synthesis ideal ℐ of U(𝓐), ℐ = k(h(𝓐 ∩ ℐ)) (hulls...
Central Idempotents in Measure Algebras.
Characterising weakly almost periodic functionals on the measure algebra
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 . In this paper, we investigate properties of . We present a short proof that 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...
Closed Ideals in Subalgebras of Banach Algebras II: Ditkin's Condition.