Related papers: Kirchberg's factorization property for locally com…

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view…

A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine…

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic…

Given a particular collection of categorical axioms, aimed at capturing properties of the category of locales, we show that if $\mathcal{C}$ is a category that satisfies the axioms then so too is the category $[ G, \mathcal{C}]$ of…

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the \beta-compactification of G (which is a G-space in a natural way), and their minimal closed…

We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and…

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive…

Let $G$ be a locally compact group. For every $G$-flow $X$, one can consider the stabilizer map $x \mapsto G_x$, from $X$ to the space $\mathrm{Sub}(G)$ of closed subgroups of $G$. This map is not continuous in general. We prove that if one…

We investigate when discrete, amenable groups have $C^*$-algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse in an open problem. We show that if $C^*(G)$ has real rank zero, then…

Let $X$ be a Banach space and let $C$ be a closed convex bounded subset of $X$. It is proved that $C$ is weakly compact if, and only if, $C$ has the {it generic} fixed point property ($\mathcal{G}$-FPP) for the class of $L$-bi-Lipschitz…

We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series -…

We study algebraic and topological properties of the convolution semigroups of probability measures on a topological groups and show that a compact Clifford topological semigroup $S$ embeds into the convolution semigroup $P(G)$ over some…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

We study the group $C^*$-algebras $C^*_{L^{p+}}(G)$ - constructed from $L^p$-integrability properties of matrix coefficients of unitary representations - of locally compact groups $G$ acting on (semi-)homogeneous trees of sufficiently large…

In this article we study MF-property for countable discrete groups, i.e. groups which admit embedding into unitary group of $C^*$-algebra $\prod M_n/\oplus M_n$. We prove that Baumslag group $\langle a,b|a^{a^b}=a^2\rangle$ has MF-property…

The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$. Under the assumption that…

We introduce the notion of relative topological principality for a family $\{H_\alpha\}$ of open subgroupoids of a Hausdorff \'etale groupoid $G$. The C*-algebras $C^*_r(H_\alpha)$ of the groupoids $H_\alpha$ embed in $ C^*_r(G)$ and we…

Let $\Delta$ be a closed, cocompact subgroup of $G \times \widehat{G}$, where $G$ is a second countable, locally compact abelian group. Using localization of Hilbert $C^*$-modules, we show that the Heisenberg module…

This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G}$ induces an isomorphism of…