相关论文: On iterated powers of positive definite functions

In this paper, we show that if the reduced Fourier-Stieltjes algebra $B_{\rho}(G)$ of a second countable locally compact group $G$ has either weak* fixed point property or asymptotic center property, then $G$ is compact. As a result, we…

This paper gives a first step toward extending the theory of Fourier-Stieltjes algebras from groups to groupoids. If G is a locally compact (second countable) groupoid, we show that B(G), the linear span of the Borel positive definite…

Let $G$ be a profinite group. A strongly admissible smooth representation $\rho$ of $G$ over $\mathbb{C}$ decomposes as a direct sum $\rho \cong \bigoplus_{\pi \in \mathrm{Irr}(G)} m_\pi(\rho) \, \pi$ of irreducible representations with…

We consider the {\it concentration functions problem} for discrete quantum groups; we prove that if $\mathbb{G}$ is a discrete quantum group, and $\mu$ is an irreducible state in $l^1(\mathbb{G})$, then the convolution powers $\mu^n$,…

We develop the concept of weak tracial Rokhlin property for finite group actions on simple (not necessarily unital) C*-algebras and study its properties systematically. In particular, we show that this property is stable under restriction…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…

Given a locally compact group $G$ and a unitary representation $\rho:G\to U({\mathcal H})$ on a Hilbert space ${\mathcal H}$, we construct a $C^*$-correspondence ${\mathcal E}(\rho)={\mathcal H}\otimes_{\mathbb C} C^*(G)$ over $C^*(G)$ and…

If $G$ is a locally compact groupoid with a Haar system $\lambda$, then a positive definite function $p$ on $G$ has a form $p(x)=< L(x)\xi(d(x)),\xi(r(x))>$, where $L$ is a representation of $G$ on a Hilbert bundle ${\h}=(G^0,\{H_u\},\mu)$,…

We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case $G = F \times \mathbb{T}^r$, with $r \in \mathbb{N}$ and $F$ finite. The characterisation obtained for…

For the Higman reversing operation $\rho$ and for a set of integer-valued functions $\mathcal X$ the following has been proved. Let the subgroup $A_{\mathcal X}$ be benign in the free group $F$, let the respective finitely presented…

We prove two versions of Bochner's theorem for locally compact quantum groups. First, every completely positive definite "function" on a locally compact quantum group $\G$ arises as a transform of a positive functional on the universal…

$\mathop{\rm rp}\nolimits ({\mathbb B})$ denotes the reduced power ${\mathbb B}^\omega /\Phi$ of a Boolean algebra ${\mathbb B}$, where $\Phi$ is the Fr\'{e}chet filter $\Phi$ on $\omega$. We investigate iterated reduced powers…

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…

For a locally compact group $G$, the first-named author considered the closed subspace $a_0(G)$ which is generated by the pure positive definite functions. In many cases $a_0(G)$ is itself an algebra. We illustrate using Heisenburg groups…

We prove that if $\rho: A(H) \to B(G)$ is a homomorphism between the Fourier algebra of a locally compact group $H$ and the Fourier-Stieltjes algebra of a locally compact group $G$ induced by a mixed piecewise affine map $\alpha : G \to H$,…

Let $G$ be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual $\Gamma$ is partially ordered. Let $\Gamma^{+}\subset\Gamma$ be the semigroup of positive elements in $\Gamma$. The Hardy space…

Let $A$ and $B$ be unital $C^*$-algebras and let $H$ be a finite dimensional $C^*$-Hopf algebra. Let $H^0$ be its dual $C^*$-Hopf algebra. Let $(\rho, u)$ and $(\sigma, v)$ be twisted coactions of $H^0$ on $A$ and $B$, respectively. In this…

A classical theorem of Herglotz states that a function $n\mapsto r(n)$ from $\mathbb Z$ into $\mathbb C^{s\times s}$ is positive definite if and only there exists a $\mathbb C^{s\times s}$-valued positive measure $d\mu$ on $[0,2\pi]$ such…

Let $G$ and $T$ be topological groups, $\alpha : T \to \Aut(G)$ a homomorphism defining a continuous action of $T$ on $G$ and $G^\sharp := G \rtimes_\alpha T$ the corresponding semidirect product group. In this paper we address several…

Let G be a locally compact group and let $\phi$ be a positive definite function on G with $\phi(e)=1$. This function defines a multiplication operator $M_\phi$ on the Fourier algebra $A(G)$ of $G$. The aim of this paper is to classify the…