On a covering group theorem and its applications.
On a generalization of Abelian sequential groups
Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group is a dense -closed subgroup of the compact group , where is the group G with the discrete...
On a method of determining supports of Thoma's characters of discrete groups
We present a new approach to determining supports of extreme, normed by 1, positive definite class functions of discrete groups, i.e. characters in the sense of E. Thoma [8]. Any character of a group produces a unitary representation and thus a von Neumann algebra of linear operators with finite normal trace. We use a theorem of H. Umegaki [9] on the uniqueness of conditional expectation in finite von Neumann algebras. Some applications and examples are given.
On character amenable Banach algebras
We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...
On characterized subgroups of Abelian topological groups and the group of all -valued null sequences
Let be an Abelian topological group. A subgroup of is characterized if there is a sequence in the dual group of such that . We reduce the study of characterized subgroups of to the study of characterized subgroups of compact metrizable Abelian groups. Let be the group of all -valued null sequences and be the uniform topology on . If is compact we prove that is a characterized subgroup of if and only if , where and is a finite Abelian group. For every compact Abelian...
On duals of Lie groups made discrete.
On functions with scattered spectra on lea groups
On infinitely small orbits
On Integrable Representations.
On LCA groups each of whose characters is ultimately measurable
On Local Central Lacunary Sets for Compact Lie Groups.
On Mackey topology for groups
The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework...
On Separation in Reduced Duals of Groups with Compact Invariant Neighbourhoods of the Identity.
On the behaviour of sequences in the dual of a nilpotent Lie group.
On the support of the conjugation representation for solvable locally compact groups.
Open subgroups and Pontryagin duality.