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Wednesday, 4 November 2026: 4 new papers, 5 cross-lists and 5 replacements in Operator Algebras (math.OA), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
We construct C*-diagonals in all UCT Kirchberg algebras. Together with known constructions of C*-diagonals in the stably finite setting by Xin Li, this shows that every classifiable C*-algebra (in the sense of the Elliott classification programme) has a C*-diagonal. In fact, we show that every UCT Kirchberg algebra admits an untwisted principal \'etale groupoid model with a finite-dimensional unit space.
In this paper, we prove that every super McDuff $\rm II_1$ factor is uniformly super McDuff. In particular, the classes of super McDuff and uniformly super McDuff $\rm II_1$ factors coincide. This answers \cite[Question D]{GJKEP} affirmatively. For factors with separable predual, super McDuffness is therefore equivalent to the Brown property and is preserved under elementary equivalence, also answering \cite[Question~6.2.1]{AGK22} affirmatively. We further show that every infinite tensor product of non-$\Gamma$ $\mathrm{II}_1$ factors is uniformly super McDuff. For a finite tensor product of separable $\mathrm{II}_1$ factors that is super McDuff, each tensor factor is either non-$\Gamma$ or uniformly super McDuff, and at least one is uniformly super McDuff.
Let $(\mathcal M_n)_{n\geqslant 1}$ be a sequence of type $\mathrm{II}_1$ factors with property $\Gamma$ and let $\omega$ be a free ultrafilter on $\mathbb N$. 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. In particular, the ultrapower $\mathcal R^\omega$ of the hyperfinite type $\mathrm{II}_1$ factor $\mathcal R$ is not a group factor.
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 $|q_{ij}|\le1$. We prove that every central element is supported on the singleton components of the strict graph of $Q$ and on its two-vertex components $\{a,b\}$ with $q_{aa}=q_{bb}=-1$ in terms of the graph-theoretic language. We also determine the spectral laws of some central elements.
We investigate connections between operator spectra, complex dynamics, and determinants for wreath product groups. For a nontrivial finite abelian group $G$, the natural action of $G\wr\mathbb Z$ on a rooted tree produces a family of operators with a recursive structure. Applying Schur complements to this family yields a rational map on complex projective space. We determine the projective spectrum--the parameter values for which the operator pencil fails to be invertible--as the union of the Julia set of this map and an explicitly described subset of its Fatou set. We also prove that the associated Koopman representation and the left regular representation are weakly equivalent and therefore give the same projective spectrum. We then compute Fuglede--Kadison determinants for a family of operators on more general wreath products. These formulas yield injective operators with zero determinant for wreath products $K\wr\mathbb Z$, where $K$ is a discrete group admitting a nontrivial projection $e\in\mathbb C[K]$. This answers negatively a question of Li and Thom about whether injectivity implies positive determinant for operators defined by matrices over complex group rings of amenable groups. For $G_{tf}\rtimes_\sigma\mathbb Z$, where $G_{tf}$ is any countable torsion-free abelian group and $\sigma\in\operatorname{Aut}(G_{tf})$, we prove that injectivity does imply positive determinant in every matrix size.
We extend Brown's one-variable rigidity theorem to strictly convex functions of two variables under a regularity assumption. Let $K\subset\mathbb{R}^2$ be nonempty, compact, and convex, and let $f$ be real-valued, strictly convex on $K$, and of class $C^2$ on a neighbourhood of $K$. We prove that the generating set $\{x_1,x_2,f\}$ is hyperrigid in $C(K)$.
The algebraic and environmental characteristics of mixed unitary quantum operations are investigated. It is established that the composition of two uniformly n-mixed unitary channels is itself n-noisy, and this n-noisy property is shown to be an invariant under unitary equivalence. Furthermore, by utilizing majorization and the divisibility of Kraus rank-four unital qubit channels, we demonstrate that any unital qubit channel can be physically simulated using a three-dimensional maximally mixed environment. Together, these results advance the classification and physical realization of noisy quantum channels.
Let $H$ be a complex Hilbert space. We prove that the class of pseudo-Fredholm operators on $H$ is a regularity in the sense of Kordula and M\"uller. We also prove that the classes of left and right generalized Drazin invertible operators are regularities on $H$. Consequently, the generalized Kato spectrum and the corresponding generalized Drazin spectra satisfy the spectral mapping theorem. We construct an operator $T$ on a separable complex Banach space such that $T^2$ is right generalized Drazin invertible whereas $T$ is not pseudo-Fredholm. In particular, the power axiom need not hold for pseudo-Fredholm operators on Banach spaces. Finally, we show that the accumulation sets of the approximate point and surjectivity spectra define regularities on Banach spaces, yielding another proof of the regularity of generalized Drazin invertible operators in $\B(X)$.
How can noncommuting quantum observables retain the geometry of a classical phase space? 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. Under the hypotheses of their AMU theorems, nonempty synthetic spectra yield AMU states. For sufficiently small $\hbar$, the position--momentum spectrum fills the plane, while the angular-momentum spectrum contains any prescribed ball. The latter calculation leads to compact Lie groups: we prove that highest-weight coadjoint orbits lie in regional synthetic spectra under an explicit variance bound. Function-space representations of $SU(n)$, $SO(n)$, and $Sp(n)$ provide further examples.