Related papers: Nonassociative $\mathrm{L}^p$-spaces and embedding…

We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \h_1. We further extend…

We show that the following five categories are equivalent: (1) the opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales; (5)…

Around 1967, Arveson invented a striking noncommutative generalization of classical $H^\infty$, known as {\em subdiagonal algebras}, which include a wide array of examples of interest to operator theorists. Their theory extends that of the…

Let $N$ be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra $\mathfrak{n}$ having rational structure constants. We assume that $N=P\rtimes M,$ $M$ is commutative, and for all $\lambda\in…

$L^p$-cohomology of rank one symmetric spaces of noncompact type is shown to be Hausdorff for values of $p$ where this does not follow from curvature pinching. Using the multiplicative structure on $L^p$-cohomology, it is shown that no…

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset…

This article contains two rigidity type results for $\mathrm{SL}(n,\mathbb{Z})$ for large $n$ that share the same proof. Firstly, we prove that for every $p \in [1,\infty]$ different from $2$, the noncommutative $L^p$-space associated with…

It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p$-space, $1\leq p<\infty$, or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…

We continue the study of $L^p$-operator algebras associated with directed graphs initiated by Corti\~nas and Rodr\'iguez, and we establish $L^p$-analogs of both the gauge-invariant and the Cuntz-Krieger uniqueness theorems. The first of…

Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pelczynski subsequence decomposition of bounded sequences in L^p[0,1] to the case of the Haagerup L^p-spaces (1\le p<\infty).…

The famous Rosenthal-Lacey theorem asserts that for each infinite compact space $K$ the Banach space $C(K)$ admits a quotient which is either a copy of $c_{0}$ or $\ell_{2}$. The aim of the paper is to study a natural variant of this result…

In this paper, we study the noncommutative Orlicz space $L_{\varphi}(\widetilde{\mathcal{M}},\tau)$, which generalizes the concept of noncommutative $L^{p}$ space, where $\mathcal{M}$ is a von Neumann algebra, and $\varphi$ is an Orlicz…

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…

Let $A^p_\omega$ denote the Bergman space in the unit disc induced by a radial weight~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$. The positive Borel measures such that the…

The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra…

Let $M$ be a Hopf--von Neuman algebra with the predual $M_*$ and $WAP(M)$ the subspace in $M$ composed of weakly almost periodic functionals on $M_*$. The main example of such an algebra is $M=L^\infty(\mathbb G)$ for a locally compact…

In our previous paper, "l^{p}-Version of von Neumann Dimension for Banach Space Representations of Sofic Groups," we define an extended version of von Neumann dimension for actions of a sofic group on a Banach space. This dimension was…

We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},\tau)$ for any noncommutative probability space $(\mathcal{M},\tau)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic…

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. Let $P$ be a non-commutative Poisson algebra over some algebraically closed field of…

Given a von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau,$ we consider the non commutative Arens algebra $L^{\omega}(M, \tau)=\bigcap\limits_{p\geq1}L^{p}(M, \tau)$ and the related algebras $L^{\omega}_2(M,…