35 papers
This paper investigates the local-triviality dimensions of actions on -algebras within noncommutative Borsuk-Ulam theory, demonstrating that free actions do not necessarily possess finite weak local-triviality dimensions and that these invariants can exhibit discontinuity or exceed fiber values in continuous fields, while establishing conditions for upper semicontinuity through examples involving noncommutative tori and spheres.
This paper introduces a canonical -algebra of operators with finite dynamical propagation for non-singular group actions, establishing its isomorphism to the algebraic crossed product under free actions to characterize ergodicity and to describe the Roe algebras of warped spaces and warped cones.
This paper investigates the Martin boundary of space-time Markov chains associated with finitely supported random walks to establish structural connections between various compactifications and harmonic function boundaries, ultimately demonstrating that the noncommutative Shilov boundary of the associated tensor algebra coincides with its Toeplitz -algebra.
This paper establishes a free probability analogue of Obata's rigidity theorem by proving that under a non-commutative curvature-dimension condition, the saturation of Voiculescu's free Poincaré inequality forces the underlying von Neumann algebra to split off a freely complemented semicircular component, thereby extending classical Gaussian splitting phenomena to the non-commutative setting.
This paper introduces a canonical Polish groupoid constructed from the unitary group and dual space of a separable unital C*-algebra, demonstrating that for Type I algebras, the associated reduced groupoid C*-algebra is Morita equivalent to the original algebra tensored with compact operators and admits a canonical diagonal embedding that characterizes commutativity.
This paper establishes sufficient conditions for the existence and uniqueness of traces on the essential and full -algebras of (possibly non-Hausdorff) étale groupoids extending invariant measures, particularly linking uniqueness to essential freeness and amenability of isotropy groups, with applications to gauge-invariant algebras of finite-state self-similar groups.
This paper establishes the continuity of derivations over a class of Banach algebras containing dense -like subalgebras, specifically demonstrating that every derivation on the -crossed product is continuous when the group is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space .
This paper establishes that unital graph C*-algebras frequently decompose into amalgamated free products, a structural insight used to fully characterize their residual finite-dimensionality and operator norm stability.
This paper establishes that the internal graph of an H-rigid graph is an isomorphism invariant for the corresponding graph product of hyperfinite II-factors, enabling the classification of such factors for specific graph types and bounding the radius difference between isomorphic graph products by one, utilizing the resolution of the Peterson-Thom conjecture.
This paper investigates the generalized Davis-Wielandt radius of Hilbert space operators by establishing new lower bounds for both this radius and the numerical radius, while also deriving an alternative to the triangular inequality for operators.
This paper establishes a homology theory for ample groupoids using compactly supported Moore complexes, proving functoriality and Kakutani invariance, deriving Mayer-Vietoris sequences, and demonstrating that a universal coefficient theorem holds for discrete coefficients while identifying specific obstructions for non-discrete ones.
This paper establishes that the uniqueness of quantum state purifications up to local unitary transformations is mathematically equivalent to Haag duality (), demonstrating that this uniqueness can fail in infinite-dimensional systems even when local tomography is possible.
This paper extends Nielsen's Theorem on LOCC ordering to bipartite quantum systems described by commuting von Neumann algebras, establishing a one-to-one correspondence between the classification of factors (types I, II, and III) and their operational entanglement properties, such as infinite single-shot entanglement and the ability to transition between arbitrary pure states with arbitrary precision.
This paper develops a theory of quantum cellular automata over arbitrary commutative rings and uses algebraic K-theory to construct a spectrum that classifies these automata up to quantum circuits and stabilization, revealing a deep connection between their classification on Euclidean lattices and the K-theory of Azumaya algebras.
This paper derives explicit analytic sufficient conditions for the Kadison--Schwarz property of unital positive linear maps on by utilizing the Bloch--Gell--Mann representation and Lie algebra structure to reduce the problem to estimates involving only the symmetric tensor , thereby establishing criteria weaker than complete positivity without relying on numerical optimization.