On Closed Ideals in the Motion Group Algebra.
Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence such that for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological...
Let be a Polish group with an invariant metric. We characterize those probability measures on so that there exist a sequence and a compact set with for all .
Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.
Let P(z,β) be the Poisson kernel in the unit disk , and let be the λ -Poisson integral of f, where . We let be the normalization . If λ >0, we know that the best (regular) regions where converges to f for a.a. points on ∂ are of nontangential type. If λ =0 the situation is different. In a previous paper, we proved a result concerning the convergence of toward f in an weakly tangential region, if and p > 1. In the present paper we will extend the result to symmetric spaces X of...
Let be the left convolution operators on with support included in F and denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that , and are as big as they can be, namely have as a quotient, where the ergodic space W contains, and at times is very big relative to . Other subspaces of are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.
We prove that for every compact, connected group G there is a singular measure μ such that the Fourier series of μ*μ converges uniformly on G. Our results extend the earlier results of Saeki and Dooley-Gupta.
The convolution kernels on a homogeneous space , where is a compact sub-group of , that satisfy the complete maximum principle are characterized.Deny’s result for abelian groups , but with a stronger hypothesis, is a special case.
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...