Related papers: Hypercontractivity for free products
We establish a free analogue of Obata's rigidity theorem. More precisely, Cheng and Zhou (2017) proved that on a weighted Riemannian manifold, the sharp spectral gap (Poincar\'e constant) is achieved only when the space splits isometrically…
We investigate the structures of crossed products of the Cuntz algebra ${\mathcal O}_\infty$ by quasi-free actions of abelian groups. We completely determine their ideal structures and compute the strong Connes spectra and K-groups.
For $n\in\mathbb{N}$, let $\{X^n_i\}$ be an infinite collection of Brownian particles on the real line where the leftmost particle $\min_iX^n_i(t)$ is given a drift $n$, and let $\mu^n_t=n^{-1}\sum_i\delta_{X^n_i(t)}$, $t\ge0$ denote the…
For every Lie group $G$, we compute the maximal $n$ such that an $n$-fold product of nonabelian free groups embeds into $G$.
Climenhaga showed the applicability of Bowen equation to arbitrary subset of a compact metric space. The main purpose of this paper is to generalize the main result of Climenhaga to free semigroup actions for non-compact sets. We introduce…
We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous…
If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a…
In the paper, we provide some examples of MF algebras by considering minimal or maximal tensor products of MF algebras and crossed products of MF algebras by finite groups or an integer group. We also present some examples of…
We develop a relative boundary theory for actions of discrete groups on compact spaces and use it to derive rigidity results for reduced crossed products. For a discrete group $\Gamma$ acting on a compact space $X$ and a subgroup $H$, we…
We investigate Friedl-L\"uck's universal $L^2$-torsion for descending HNN extensions of finitely generated free groups, and so in particular for $F_n$-by-$\mathbb{Z}$ groups. This invariant induces a semi-norm on the first cohomology of the…
In this paper we describe the amalgamated free product of two hyperfinite von Neumann algebras over a finite dimensional subalgebra. In general the free product is a finite direct sum of interpolated free group factors and a hyperfinite von…
An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_1$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states.…
We classify torsion actions of free wreath products of arbitrary compact quantum groups and use this to prove that if $\mathbb{G}$ is a torsion-free compact quantum group satisfying the strong Baum-Connes property, then…
A suitable notion of hypercontractivity for a nonlinear semigroup $\{T_t\}$ is shown to imply Gagliardo--Nirenberg inequalities for its generator $H$, provided a subhomogeneity property holds for the energy functional $(u,Hu)$. We use this…
We develop a variational approach in order to study the qualitative properties of non-autonomous parabolic equations. Based on the method of product integrals, we discuss long-time behavior, invariance properties, and ultracontractivity of…
We introduce a framework allowing for key aspects of deformation/rigidity theory to be used in the study of continuous model theory of II$_1$ factors. Using this framework, we solve several well-known open problems in the area. For example,…
This paper provides a new tauberian approach to the study of quantitative time asymptotics of collisionless transport semigroups with general diffuse boundary operators. We obtain an (almost) optimal algebraic rate of convergence to…
Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a…
The main result of this paper is a generalization of Popa's free independence result for subalgebras of ultraproduct ${\rm II_1}$ factors [Po95] to the framework of ultraproduct von Neumann algebras $(M^\omega, \varphi^\omega)$ where $(M,…
We give new and improved results on the freeness of subgroups of free profinite groups: A subgroup containing the normal closure of a finite word in the elements of a basis is free; Every infinite index subgroup of a finitely generated…