Related papers: Realization of compact spaces as cb-Helson sets

In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we actually obtain a real and finitely summable spectral triple…

For a $C^*$-algebra $A$ of compact operators and a compact manifold $M,$ we prove that the Hodge theory holds for $A$-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective $A$-Hilbert…

Let $\mathcal{X}_S$ denote the class of spaces homeomorphic to two closed orientable surfaces of genus greater than one identified to each other along an essential simple closed curve in each surface. Let $\mathcal{C}_S$ denote the set of…

We show that for any connected smooth manifold $M$ of dimension different from $3$ the restriction of the compact-open topology to the diffeomorphism group of $M$ is minimal, i.e. the group does not admit a strictly coarser Hausdorff group…

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…

For a compact surface $\Sigma$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $\operatorname{Fix} B$, of any family $B$ of endomorphisms of $\pi_1(\Sigma)$ is compressed in $\pi_1(\Sigma)$ i.e.,…

We extend the classical theory of homotopical $\Sigma$-sets $\Sigma^n$ developed by Bieri, Neumann, Renz and Strebel for abstract groups, to $\Sigma$-sets $\Sigma_{\mathrm{top}}^n$ for locally compact Hausdorff groups. Given such a group…

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui's definition of the topological full group from the compact, to the locally compact case. We provide two general classes of groupoids for…

We prove a compactness result for classes of actions of many small categories on quantum compact metric spaces by Lipschitz linear maps, for the topology of the covariant Gromov-Hausdorff propinquity. In particular, our result applies to…

Let $M=G/H$ be a compact, simply connected, Riemannian homogeneous space, where $G$ is (almost) effective and $H$ is a simple Lie group. In this paper, we first classify all $G$-naturally reductive metrics on $M$, and then all $G$-geodesic…

The category of locally compact quantum groups can be described as either Hopf $*$-homomorphisms between universal quantum groups, or as bicharacters on reduced quantum groups. We show how So{\l}tan's quantum Bohr compactification can be…

In this article, the class of all Dunford-Pettis $ p $-convergent operators and $ p $-Dunford-Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces $ X $ and $ Y $ such that…

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.

Recall that a topological space is said to be a $k_\omega$-space if it is the direct limit of an ascending sequence of compact Hausdorff topological spaces. If each point in a Hausdorff space $X$ has an open neighbourhood which is a…

We classify $C$-orderable groups admitting only finitely many $C$-orderings. We show that if a $C$-orderable group has infinitely many $C$-orderings, then it actually has uncountably many $C$-orderings, and none of these is isolated in the…

Let G be a reductive complex Lie group with Lie algebra g. We call a subgroup H of G {\bf cramped} if there is an integer b(G,H) such that each finite dimensional representation of G has a non-trivial invariant subspace of dimension less…

A result of Gilbert shows that every completely bounded multiplier $f$ of the Fourier algebra $A(G)$ arises from a pair of bounded continuous maps $\alpha,\beta:G \rightarrow K$, where $K$ is a Hilbert space, and $f(s^{-1}t) =…

A version of Arzel\`a-Ascoli theorem for $X$ being $\sigma$-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and…

Let a group $\Gamma$ act on a paracompact, locally compact, Hausdorff space $M$ by homeomorphisms and let $2^M$ denote the set of closed subsets of $M$. We endow $2^M$ with the Chabauty topology, which is compact and admits a natural…

We show that if $E$ is a closed convex set in $\mathbb C^n$ $(n>1)$ contained in a closed halfspace $H$ such that $E\cap bH$ is nonempty and bounded, then the concave domain $\Omega = \mathbb C^n\setminus E$ contains images of proper…