Second copy never unlocks Werner-state distillation
A sharp projection estimate proves the 2-copy threshold matches the 1-copy threshold in every dimension.
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Operator Algebras
Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry
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Matrix rule decides which C*-subalgebras are regular
In finite dimensions, the same row/column pattern that governs unitary regularity already decides plain regularity.
· “A Complete Characterization of Regular Inclusions of Finite Dimensional C^*-algebras”
Quantum steering equals state-preserving conditional expectations
Algebra inclusions decide which side can steer which—not tomography.
· “Quantum steering is equivalent to state-preserving conditional expectations”
All invariant C*-subalgebras of PSL_n(Z) arise from normal subgroups
For n≥3, PSL_n(Z)'s reduced C*-algebra has no exotic invariant subalgebras — rigidity matches the von Neumann case.
Arctangent commutator is positive
A trace-class operator with trace π/2 shows a positive commutator need not fit Kato's sufficient condition.
· “A counterexample to the Kato conjecture for positive commutators”
Approximation numbers tied to Hilbert numbers: a_n ≤ e(n+1) h_n
Settles 60-year-old conjectures of Carl, Pietsch, Mityagin and Henkin up to the constant e.
· “On bounds between all s-numbers and widths of convex sets”
Separable type II1 factors gain orthonormal bases of self-adjoint unitaries
This settles Kadison's 1967 question for all separable diffuse finite von Neumann algebras.
· “The separable case of Kadison's problem on orthonormal bases of unitaries for type II₁ factors”
A researcher has built a map connecting the topology of infinite-dimensional manifolds to…
For Hilbert manifolds with bounded geometry, the paper constructs a homomorphism from geometric K-homology to the K-theory of the…
· “Geometric K-homology and operator K-theory for Hilbert manifolds”
Subadditive weight refutes 1975 normality problem
On the algebra of all bounded operators, directed suprema survive while σ-weak limits do not.
· “A counterexample to Haagerup's problem on subadditive weights”
Dephasing graph on M_n yields the Cuntz algebra O_n
Explicit sums of renormalized generators yield the Cuntz isometries that generate the entire local quantum algebra.
· “Local quantum Cuntz--Krieger algebras of dephasing quantum graphs”
One constant sets entropy decay on every classical and quantum torus
A matrix-valued Wirtinger inequality pins the sharp rate at 1 in every dimension and deformation.
· “Sharp Complete Modified Log-Sobolev Inequalities on Classical and Quantum Tori”
Completion of a continuous inverse algebra can break the CIA property
Inversion stays continuous, but invertible elements fail to form an open set after completion.
· “The completion of a continuous inverse algebra need not be a continuous inverse algebra”
This paper proves a factorization theorem for normalizing unitaries in commuting squares…
A relative eigenbasis property is shown to be necessary and sufficient for regularity of the crossed-product inclusion N⋊G⊆M⋊G, while…
· “Structural and Dynamical Properties of Subfactor Commuting Squares”
First K-theory gap between Roe and quasi-local algebras
For high-girth expanders, the inclusion between the two algebras fails to be surjective on K_0.
· “K-Theoretic Comparison of Roe and Quasi-Local Algebras via Projections”
Tree shape, not orientation, decides bivariant K-theory
Reflection functors make KK(X)_loc and the bootstrap category depend only on the underlying tree of X.
Free and Boolean rare events now have explicit error rates
Boolean error is at most 2 times sum p^2; free error at most 3 times sum p^(3/2).
A Fell bundle is Haagerup exactly when its C*-algebra is
For any state on the unit fiber, the bundle and its algebra are Haagerup together; twisted crossed products follow.
Two-parameter Rényi divergence equals an average of relative entropies
Every α–z divergence is a probability average of escort-state relative entropies, plus a boundary term when supports are not nested.
Complete symbols exist on noncompact symmetric spaces
Equivariant operators are exactly multipliers by Harish-Chandra symbols when kernels decay away from the diagonal.
· “Complete Symbols of Equivariant Pseudodifferential Operators on Noncompact Symmetric Spaces”
Petz recovery map is Bayesian inversion for quantum systems
For von Neumann algebras, it obeys the same compositional and time-reversal laws as Bayes' rule.
· “Bayesian inference and retrodiction for faithful states on von Neumann algebras”
Operators that are minimum attaining on reducing subspaces are dense
Every bounded operator on a separable Hilbert space is a norm limit of such operators.
· “Minimum attaining operators on reducing subspaces: Spectral structure and density”
Good measure simplices are realized by minimal homeomorphisms
Clopen evaluations build a dimension group whose order interval is exactly the clopen sets.
· “Affine Evaluation Maps, Dimension Groups, and Fair measures”
Every type I_k operator has the norm convergence property
A projection sandwich extends decomposability from matrices to all finite type I von Neumann algebras.
· “Decomposability and Norm Convergence Property of Operators in Type I_k von Neumann Algebras”
Every nonseparable type II$_1$ factor has a unitary basis
The paper closes the nonseparable half of Kadison's 1967 problem on unitary bases.
· “The nonseparable case of Kadison's problem on orthonormal bases of unitaries for type II₁ factors”
Maximal pure states force maximality in a new Choquet-type order
The amendment recovers the tight-extension rigidity theorem and matches the classical Choquet order in the commutative case.
· “Choquet-Type Relations and a State Space Level Amendment of Arveson's Hyperrigidity Conjecture”
Trace-scaling flows on full factors: one or continuum-many
The count decides how many type III1 factors share a given continuous core.
· “Non-uniqueness of continuous trace-scaling flows on certain full factors”
Averaging unitaries yields quantum channels on full state spaces
Construction works for non-normal states, extending Schrödinger-picture channels beyond finite dimensions.
· “Quantum channels on duals of von Neumann algebras in the Schr\"{o}dinger picture”
All complex Hadamard matrices of a fixed size are quantum equivalent
The largest quantum symmetry group erases same-size differences, while finer quantum equivalences still separate matrices.
· “Complex Hadamard Matrices - Quantum Symmetries, Equivalence and Non-Local Games”
Every diagonal AH-algebra is a transformation groupoid algebra
An action of the AF-groupoid on the diagonal's spectrum recovers the Weyl groupoid and, with it, the algebra.
Spectral Lp norm construction completed for tracial JBW*-algebras
The exceptional Albert factor now satisfies the same Minkowski inequality as all other Jordan components, closing the last open case.
Channel-state duality fails for algebras that don't mirror themselves
Without an anti-automorphism of the local algebra, no natural identification of channels with bipartite states exists.
· “Choi--Jamio{l}kowski-type isomorphisms for von Neumann algebras”
A simple C*-algebra that is not singly generated
A finite set of coordinate functions escapes every single-element subalgebra in a unital separable example.
· “A simple separable C*-algebra which is not singly generated”
PPT noise always kills entanglement after finitely many rounds
A new proof removes faithful-support assumptions and bounds many PPT maps by three channel uses.
· “Every PPT channel has finite entanglement breaking index”
Non-injective local maps satisfy dynamical comparison
Closed sets can always be dynamically moved into any open set; the resulting C*-algebras are UCT Kirchberg algebras.
One monoid exposes loop entrances and algebra type
Its order and Z^k-shifts reveal whether graph algebras are locally finite, purely infinite, or crossed products.
· “Some more talents of the talented monoid of a higher-rank graph”
Double stabilization decides graded Morita equivalence
For topologically graded C*-algebras, Morita equivalence reduces to one explicit graded isomorphism after tensoring with K twice.
Big L\'evy jumps decide free-law moment finiteness
A freely infinitely divisible law's moment growth matches that of its large free L\'evy jumps.
· “Integrability of Freely Infinitely Divisible Distributions and L\'evy Measures”
First counterexample: lamplighter word-length triples are not metric
For every d≥2 and every generating set, the diagonal operator on the lamplighter group fails to metrize the state space.
· “Word-Length Spectral Triples of (mathbb{Z}/2mathbb{Z})wrmathbb{F}_(d) Are Not Metric”
Cartan inclusions are exactly multiplicity-free matrices
Column sums decide Cartan subalgebras and unique conditional expectations.
· “A Complete Characterization of Cartan Inclusions of Finite Dimensional C^*-algebras”
Convex range means restricted integrals never injective
A Lyapunov-type theorem for quantum measurements: non-atomicity alone fails in infinite dimensions.
· “Integration Theory for Completely positive Instruments: A Lyapunov-Type Theorem and Applications”
Minimal étale groupoids are Følner or paradoxical
A new coarse-geometric notion unifies group amenability and metric amenability and yields invariant measures.
Two invariants classify all Rokhlin group kernel actions
Matching lifting obstructions and K-theory modules force conjugacy of anomalous group actions on UCT Kirchberg algebras.
· “Classification of anomalous actions of finite groups with the Rokhlin property”
One decomposition pattern makes covariance algebras universal
Free products, graph products, and Hecke algebras fall into a single framework; approximation properties follow.
One functional calculus unifies three operator smoothness results
The kth derivative of f(a+b)-f(a) is a lexicographic divided-difference sum, covering commutative, finite-dimensional, and Besov cases.
· “Lexicographic functional calculus and its application to functional calculus calculus”
Tame factorization detects the Omega property
Triples with a DN-Omega middle space: TF holds exactly when X has Omega; adding DN makes X a finite-type power series
All ℓ²-Betti numbers vanish for inner amenable groups
Higher-degree cases were open until now; a uniform finite-stage dimension argument settles them.
· “Vanishing of ell²-Betti numbers for inner amenable groups”
Boundary crossed products have no hidden intermediate algebras
For rank-one product lattices, the intermediate C*-algebras are exactly the coordinate crossed products.
· “The noncommutative topological factor theorem for rank-one product lattices”
Bogoliubov free-energy bound reaches infinite systems
New theorem bounds the cost of separating subsystems by two energy averages, giving a thermodynamic route to entanglement.
Inner scaling automorphisms force Kac type
Resolves a conjecture: compact quantum groups with all scaling automorphisms inner must have tracial Haar measure.
Two non-isomorphic algebras share K-theory once κ is dropped
For unbounded torsion in K1, the κ maps are no longer redundant in classification.
· “Bockstein operations and AD algebras with unbounded torsion in K₁”
Phantom E-theory classes form a derived inverse limit
A Milnor sequence computes the invisible part of E-theory for all separable C*-algebras.
Free sums match the classical Berry–Esseen rate
The Kolmogorov error to the semicircle law has the same Lyapunov-fraction form as in the classical case.
· “The Berry--Esseen Estimate in the Free Central Limit Theorem”
Singular rings get explicit motivic cohomology
Truncated polynomial rings over number fields now have a closed-form integral motivic cohomology.
Five rays kill subhomogeneity in dimension three
A pentagon's free polyhedron has irreducible boundary points at every even level, so no finite matrix bound exists.
Strong amenability + no property (T) = a non-continuous semigroup
The same equivalence handles the Haagerup case and is new even for classical locally compact groups
· “Amenability of locally compact quantum groups via the long-time behavior of convolution semigroups”
Heisenberg net reps form a continuous Tambara-Yamagami category
Twisted and untwisted sectors match TY(R, χ_-, +1), the first direct-integral fusion computation for a conformal net.
Projection triples on disk spaces forced into three shapes
On Hardy, Bergman, Bloch and vector-valued spaces, these projections are cube-root isometries or bi-circular ones.
· “Generalized tri-circular projections on some spaces of analytic functions”
Symmetrized polydisc gets a Schur-Agler realization theorem
Functions on the symmetrized polydisc reduce to unitary-colligation form, yielding interpolation, corona, extension.
· “Function theoretic aspects of the symmetrized polydisc and generalization”
Hexablock Schur-Agler class equals unitary colligations
A single kernel positivity test yields interpolation, extension, and corona theorems for the biball and tetrablock.
· “Function theory of the hexablock and applications to the tetrablock and Euclidean biball”
Unique ergodicity pins down unique extensions in crossed products
For abelian group actions, a single invariant state forces a single pseudo-expectation on the reduced crossed product.
Spectral gap on line bundles reaches limit 1
Closed hyperbolic 3-manifolds of growing volume get two-torsion line bundles whose smallest Laplace eigenvalue tends to 1.
· “Near optimal spectral gaps for line bundles on hyperbolic three-manifolds”
Extensions by exact groups get strong matrix approximations
A double crossed-product trick extends finite-dimensional unitary models to semidirect, wreath, and free-by-cyclic groups.
· “Strongly converging unitary representations for extensions by exact groups”
Operator systems and their duals are mutual inverses when tight
Tightness guarantees S ≅ (S^d)# and V ≅ (V#)^d, covering unital operator systems and C*-algebras.
Nonnuclear free-group odometers still give pure C*-algebras
Simple monotracial crossed products keep real rank zero and selflessness without nuclearity or Z-stability
Twists force kernels
Many unitaries admit only product-zero pairs; twisted unitaries come from equivalent commuting factors
Symmetry breaking splits topological indices into weak and strong
Only the strong quotients can control quantized macroscopic observables
One subset notion unifies quantum graph colouring and components
Projective subsets make classical definitions transfer verbatim and restore lost dualities
Purely infinite graph algebras get nuclear dimension one
The result holds even for non-simple algebras, by reading purity off the graph's cycles and tails.
· “Nuclear dimension, pure infiniteness and real rank for higher rank graph C^*-algebras”
Operator systems are modules over matrix algebras
Enriched category theory turns the scalar-action analogy into a precise equivalence and recovers classical theorems
· “Nonunital Operator Systems as Modules in Enriched Category Theory”
One Jordan-block size fixes the zero singularity of binary semicircles
Complete classification of full two-generator pencils: explicit blow-up exponent and constant at 0.
Two unitaries pin down every endomorphism of the 2-adic C*-algebra
The monoid classification resolves open extension questions and computes the Weyl group as Z(2∞)⋊Z/2.
· “Endomorphisms of the 2-adic ring C^*-algebra and its Weyl group”
Independent unitaries satisfy a free Szegő limit theorem
Expected word-series traces and random-pencil determinant averages converge to explicit formulas, settling an open conjecture.
Finite diagonal dimension passes to intermediate algebras
A product bound with the spectrum’s covering dimension recovers and extends the Archbold–Kumjian AF theorem
Quadratic growth is the cutoff for uniform property Γ
Subquadratic ASH algebras always have the property; a quadratic example shows the bound is sharp.
Operator factorizations are either clean or strange
A trace condition on defect spaces decides which, and finite-rank defects guarantee the clean case.
Two operators generate the full eigen-algebra of a triangle Jacobi basis
Every differential eigenoperator of the symmetric Jacobi basis is a unique polynomial in two second-order operators.
· “Symmetric Jacobi Polynomials on a Triangle and Their Spectral Algebra”
One injective envelope controls all ideal intersections
A system has hidden ideals exactly when its injective envelope does—tests can move to the envelope.
All primitive ideals of a p-adic crossed product identified
The ideal space splits into eight explicit strata with complete hull-kernel closure rules, settling the structure of this C*-algebra.
Lamplighter growth spectrum is affine
Counting elements by cursor height yields a closed-form rate with a second-order transition and a growth gap for the base group.
· “A phase transition in the directional growth of lamplighter groups”
Uncountable abelian subgroups break the lifting property
For uncountable abelian groups, the full C*-algebra has local lifting but no global lifting, separating LP from LLP.
· “Uncountable Abelian Group C*-algebras Fail the Lifting Property”