Ambitable topological groups

Detecting topological groups which are (locally) homeomorphic to LF-spaces

We present a simple-to-apply criterion for recognizing topological groups that are (locally) homeomorphic to LF-spaces.

A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More precisely, we use of a version of the remarkable Riesz-Kantorovich formulae and Fatou property for bounded order bounded homomorphisms to allocate the desired structures. Moreover, we show that unbounded convergence on a locally solid lattice group is topological and we investigate some applications of it. Also, some necessary and sufficient conditions for compl…

Abstract harmonic analysis on locally compact right topological groups

Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this paper, we broaden the scope of this work. We give (similar) sufficient conditions for the existence of a Haar measure on locally compact right topological groups and generalize analytic theory to this setting. We then define new measure algebra analogues in the compact setting and use these to completely characterize the existence of a Haar measure, producing…

拓扑群作用的可均性与斜可均性

Amenability and skew-amenability of actions of topological groups

本文定义并研究拓扑群在紧空间上连续作用的可均性与斜可均性，旨在解决可均性向闭子群传递的条件，并应用于泛最小流分析。

Some remarks on convex analysis in topological groups

We discuss some key results from convex analysis in the setting of topological groups and monoids. These include separation theorems, Krein-Milman type theorems, and minimax theorems.

Representations of 2-transitive topological groups

An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group and representation space are noncompact the representation is irreducible

A few remarks on boundedness in topological modules and topological groups

Let X, Y, and Z be topological modules over a topological ring $R$. In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\times Y$ into $Z$ with respect to the three different uniform convergence topologies. We show that these spaces form again topological modules over $R$. In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.

拓扑满群、可逆等距与广群代数的自同构

Topological full groups, invertible isometries, and automorphisms of groupoid algebras

本文研究紧单位空间Hausdorff丰沛广群的拓扑满群与对应伪函数代数可逆等距同伦类群的关系，并给出有效广群下伪函数代数自同构群的分裂扩张结构。

Abelian topological groups without irreducible Banach representations

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.