Related papers: Zero divisors and L^p(G), II

We consider two questions on the geometry of Lipschitz free $p$-spaces $\mathcal F_p$, where $0<p\leq 1$, over subsets of finite-dimensional vector spaces. We solve an open problem and show that if $(\mathcal M, \rho)$ is an infinite…

We begin with the existence of groups with trivial duals for cardinals aleph_n (n in omega). Then we derive results about strongly aleph_n-free abelian groups of cardinality aleph_n (n in omega) with prescribed free, countable endomorphism…

If $G$ is a nilpotent group with a balanced presentation and $G\not\cong\mathbb{Z}^3$ then $\beta_1(G;\mathbb{Q})\leq2$ \cite{Hi22}. We show that if such a group $G$ has an abelian normal subgroup $A$ such that $G/A\cong\mathbb{Z}^2$ then…

We establish that finitely generated non-abelian direct products $G$ of free pro-$p$ groups have full Hausdorff spectrum with respect to the lower $p$-series $\mathcal{L}$. This complements similar results with respect to other standard…

Let $G$ be an abelian group of finite order $n$, and let $h$ be a positive integer. A subset $A$ of $G$ is called {\em weakly $h$-incomplete}, if not every element of $G$ can be written as the sum of $h$ distinct elements of $A$; in…

In this article we study cocycles of discrete countable groups with values in l^2(G) and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l^2(G) and answer several…

In this paper, we show that if $L_p$ Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a centered disk when $p\in[0,1)$. Moreover, we investigate $C^0$ estimate of…

For $p\in (1,\infty)$, we study representations of \'etale groupoids on $L^{p}$-spaces. Our main result is a generalization of Renault's disintegration theorem for representations of \'etale groupoids on Hilbert spaces. We establish a…

We use new methods, specific of non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$-Banach space for $0<p<1$ are democratic. The novel techniques we obtain permit to show in particular that all…

We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and…

We construct examples of weighted algebras $L_p^w(G)$ with $1<p\le 2$ on uncountable free groups. For $p>2$ no weighted algebras exist on these groups. From the other side, we prove that an amenable group on which exist weighted algebras…

In previous work, we defined extended versions of von Neumann dimension for Banach space representations of sofic groups. The main application was a definition of l^{p}-dimension and, using this, a proof that the actions of a countable…

We show that any bounded analytic semigroup on $L^p$ (with $1<p<\infty$) whose negative generator admits a bounded $H^{\infty}$ functional calculus with respect to some angle $< \pi/2$ can be dilated into a bounded analytic semigroup…

Let $G$ be a locally compact abelian (LCA) group. We denote by $G_{op}$, the intersection of all open pure subgroups of $G$, which we call the $OP$ subgroup of $G$. In this paper, we prove that the $OP$ subgroup of a torsion-free LCA group…

We introduce Banach algebras associated to twisted \'etale groupoids $(\mathcal{G},\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the…

Let $L$ denote a right-invariant sub-Laplacian on an exponential, hence solvable Lie group $G$, endowed with a left-invariant Haar measure. Depending on the structure of $G$, and possibly also that of $L$, $L$ may admit differentiable…

Let G be a finitely generated free, free abelian of arbitrary exponent, free nilpotent, or free solvable group, or a free group in the variety A_mA_n, and let A = {a_1,..., a_r} be a basis for G. We prove that, in most cases, if S is a…

Let G be a torsion free discrete group with a finite dimensional classifying space BG. We show that G has a dual Dirac morphism if and only if a certain coarse (co)-assembly map is an isomorphism. Hence the existence of a dual Dirac…

Let $A$ be an algebra with a right identity. In this paper, we study $(p, q)-$centralizers of $A$ and show that every $(p, q)-$centralizer of $A$ is a two-sided centralizer. In the case where, $A$ is normed algebra, we also prove that $(p,…

Let $G$ be a locally compact group and $p,q\in \mathbb{R}$ with $p>1$ $p\not=2$ and $q$ between $2$ and $p$ (if $p<2$ then $p<q<2$, if $p>2$ then $2<q<p.$) The main result of the paper is that $A_q(G)$ multiplies $A_p(G)$, more precisely we…