Closed Ideals of Homogeneous Algebras.
Comparisons of Sidon and sets
Connes amenability-like properties
We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.
Constructions of singular measures with remarkable convolution properties
Contractive homomorphisms of measure algebras and Fourier algebras
We show that the dual version of our factorization [J. Funct. Anal. 261 (2011)] of contractive homomorphisms φ: L¹(F) → M(G) between group/measure algebras fails to hold in the dual, Fourier/Fourier-Stieltjes algebra, setting. We characterize the contractive w*-w* continuous homomorphisms between measure algebras and (reduced) Fourier-Stieltjes algebras. We consider the problem of describing all contractive homomorphisms φ: L¹(F) → L¹(G).
Convolution de mesures portées par une surface convexe
Convolution operators on the dual of hypergroup algebras
Let be a hypergroup. In this paper, we define a locally convex topology on such that with the strong topology can be identified with a Banach subspace of . We prove that if has a Haar measure, then the dual to this subspace is has compact carrier}. Moreover, we study the operators on and which commute with translations and convolutions. We prove, among other things, that if is left stationary, then there is a weakly compact operator on which commutes with convolutions if and...
Corrigendum and addendum to the paper "In general, Bernoulli convolutions have independent powers", Studia Math. 47 (1973), pp. 141-152
Decomposable multipliers and applications to harmonic analysis
For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...
Dérivation sur un groupe localement compact et abélien
Derivations into iterated duals of Banach algebras
We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space is zero; i.e., . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study...
Extension de la catégorie des algèbres de Kac
On munit la classe des algèbres de Kac d’une nouvelle classe de morphismes, stable par dualité. Cela permet de rendre compte, dans les cas abélien ou symétrique, de la catégorie des groupes localement compacts munis des morphismes continus de groupe. Le lien avec les morphismes précédemment définis et beaucoup plus restrictifs est établi.
Factorisation without bounded approximate identities
Fixed point characterization of left amenable Lau algebras.
GAUSS MEASURES ON SEMIGROUPS.
Good weights for weighted convolution algebras
Weighted convolution algebras L¹(ω) on R⁺ = [0,∞) have been studied for many years. At first results were proved for continuous weights; and then it was shown that all such results would also hold for properly normalized right continuous weights. For measurable weights, it was shown that one could construct a properly normalized right continuous weight ω' with L¹(ω') = L¹(ω) with an equivalent norm. Thus all algebraic and norm-topology results remained true for measurable weights. We now show that,...
Harmonic analysis on -torsional groups
Hewitt-Zuckermann Semigroups in the Structure Semigroups of Measure Algebras.
Ideal Structure of Operator and Measure Algebras.
In general, Bernoulli convolutions have independent powers