Operator Algebras Papers of the Week

We prove that the nuclear dimension of any graph $C^*$-algebra is at most two, and we compute the exact value of the nuclear dimension for a large class of graph $C^*$-algebras.

We investigate connections between operator spectra, complex dynamics, and determinants for wreath product groups.

We construct C*-diagonals in all UCT Kirchberg algebras.

Motivated by the recent explicit counterexample to Connes' embedding conjecture, we study the degree and number of variables needed to separate normalized matrix traces on self-adjoint contractions from traces on finite von Neumann algebras.

We determine the center and characterize factoriality for mixed $q$-Gaussian von Neumann algebras associated with real symmetric matrices $Q=(q_{ij})_{i,j\in I}$ satisfying $|q_{ij}|\le1$.

Motivated by Mumford's question on approximately macroscopically unique (AMU) states and the work of Lin and Wang, we study synthetic spectra of position--momentum and angular-momentum systems.

For a Hopf-von Neumann algebra $(M,\Gamma)$, we introduce the space ${\rm WAP}_{{\rm Bessel},\pi_u}(M_*)$ through norm convergence conditions on rows and columns of slices associated with Bessel families in the universal representation.

Using minimal weak*-closed left ideals, we obtain an idempotent state \(\varphi\in\operatorname{WAP}(M_*)^*\) satisfying \(\varphi\star \omega\star\varphi=\varphi\) for every state \(\omega\) on \(\operatorname{WAP}(M_*)\).

In this paper, we prove that every super McDuff $\rm II_1$ factor is uniformly super McDuff.

In this paper, we show that the usual Hausdorff--Young inequalities for locally compact quantum groups such as the quantum \(E_q(2)\), the real quantum \(az+b\), and the extended quantum \(SU_q(1,1)\), where \(0<q<1\), are sharp.

We take a substantial step forward toward characterizing the irreducibility of the operator $M_B$ on $L_a^2(\mathbb{D})$, or equivalently, the trivialness of the von Neumann algebra $\{M_B,M_B^*\}'$.

We introduce the notion of Boomerang subalgebras of group von Neumann algebras and study their general properties.

We prove that every subfactor of the ultraproduct $\prod_\omega\mathcal M_n$ of finite Jones index is not isomorphic to the group von Neumann algebra of any discrete group.

The basic techniques involving Gaussian variables originate in OpenAI's preprint, and are also the main new tool in its proposed solution to the Toms--Winter conjecture. We extend these techniques in order to deal with the weight functions coming from amenability, and one of the main new ingredients is the fact that one can replace an amenable action by an auxiliary one for which the amenability weights are central.

We prove that a von Neumann algebra $N$ is injective if and only if $\|T\|_{\mathrm{dec}}=\|T\|_{\mathrm{cb}}$ for every linear map $T:\ell^\infty_3to N$, answering a problem of Haagerup (1985).

We study 3-tensors satisfying the ``zipper condition,'' which play an important role in tensor network approaches to two-dimensional topological order.

We establish a general principle for bounding the matrix-valued analytic functional calculus $F\mapsto F(T)$ of a Hilbert space operator $T$, independently of the matrix size.

We establish an operator-valued Fejer-Riesz factorization theorem for the algebraic free product A of C[F], the group algebra on the free group F on finitely many generators, with finitely many finite dimensional C-star algebras.

Let $(\mathcal{M},\tau)$ be a tracial von Neumann algebra, $T:L_1(\mathcal{M},\tau)\to L_1(\mathcal{M},\tau)$ be induced by a normal $\tau$-preserving $*$-automorphism of $\mathcal{M}$, and $x\in L_1(\mathcal{M},\tau)$. We will prove the bilaterally almost uniform convergence of averages of the form $$\frac{1}{n}\sum_{k=0}^{n-1}T^k(x_k),$$ generalizing an ergodic theorem proven by Breiman in \cite{Breiman57}, where $(x_k)_{k=0}^{\infty}$ is an element of the noncommutative vector-valued $L_p$-space $L_p(\mathcal{M},\tau;\ell_\infty)$ such that there exists $x\in L_p(\mathcal{M},\tau)$ with $(x_k-x)_{k=0}^{\infty}\in L_p(\mathcal{M},\tau;c_0)$.