Related papers: Ueda's peak set theorem for general von Neumann al…

We revisit Haagerup's enigmatic reduction theorem \cite[Theorems 2.1 \& 3.1]{HJX} showing how that theorem may be extended to general von Neumann algebras $\M$ equipped with an arbitrary faithful normal semifinite weight in a manner which…

Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $\Phi$. We give necessary and sufficient conditions for which $\mathfrak A$ is…

We give an affirmative answer to the question whether there exist Lie algebras for suitable closed subgroups of the unitary group $U(\mathcal{H})$ in a Hilbert space $\mathcal{H}$ with $U(\mathcal{H})$ equipped with the strong operator…

We prove that a finite von Neumann algebra ${\mathcal A}$ is semisimple if the algebra of affiliated operators ${\mathcal U}$ of ${\mathcal A}$ is semisimple. When ${\mathcal A}$ is not semisimple, we give the upper and lower bounds for the…

The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…

In his study of amenable unitary representations, M. E. B. Bekka asked if there is an analogue for such representations of the remarkable fixed-point property for amenable groups. In this paper, we prove such a fixed-point theorem in the…

We consider converses to the density theorem for irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that under the…

The peak algebra is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks. By exploiting the combinatorics of sparse subsets of [n-1] (and of certain classes of compositions…

The goal of the paper is to study a topology generated by the star order on von Neumann algebras. In particular, it is proved that the order topology under investigation is finer than $\sigma$-strong* topology. On the other hand, we show…

On a closed Riemannian manifold, we construct a family of intrinsic Gaussian noises indexed by a regularity parameter $\alpha\geq0$ to study the well-posedness of the parabolic Anderson model. We show that with rough initial conditions, the…

Using computations in the bidual of $\mathbb{B}(L^2M)$ we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of…

Let $A$ be a separable, unital and exact $C^*$-algebra satisfying the universal coefficient theorem. We prove uniqueness theorems up to unitary conjugacy for unital, full and nuclear maps from $A$ into ultraproducts of finite von Neumann…

We show that the Freiman--Ruzsa theorem, characterising finite sets with bounded doubling, leads to an alternative proof of a characterisation of Meyer sets, that is, relatively dense subsets of Euclidean spaces whose difference sets are…

It is shown that the bona fide generalization of the Vitali-Hahn-Saks Theorem to von Neumann algebras is possible if, and only if, the algebra is finite. This settles the problem on the noncommutative Vitali-Hahn-Saks Theorem completely and…

In the paper we introduce a weak set theory $\mathsf{H}_{<\omega}$ . A formalization of arithmetic on finite von Neumann ordinals gives an embedding of arithmetical language into this theory. We show that $\mathsf{H}_{<\omega}$ proves a…

Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…

We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…

Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on…

We axiomatize in (first order finitary) continuous logic for metric structures $\sigma$-finite $W^*$-probability spaces and preduals of von Neumann algebras jointly with a weak-* dense $C^*$-algebra of its dual. This corresponds to the…

We establish new metric characterizations for the norm (respectively, ultraweak) closure of the convex hull of a bounded set in an arbitrary $C^*$-algebra (respectively, von Neumann algebra), and provide applications of these results to the…