35 papers
This paper establishes dimension-free -estimates for operator-valued maximal spherical means over cyclic groups by extending the Nevo-Stein spectral technique to the noncommutative setting, thereby proving a noncommutative spherical maximal inequality for automorphism actions on von Neumann algebras.
This paper introduces a local treatment of finite alignment for arbitrary higher-rank graphs by identifying a finitely aligned sub-constellation, which enables the construction of novel locally compact path and boundary-path groupoids that extend existing models and are proven to be amenable.
This paper investigates the quantum automorphism algebra of a quantum graph associated with a simple finite graph , proving that for any graph with at least three vertices, admits nonlocal symmetry through the existence of a perfect quantum no-signaling correlation.
Motivated by recent finite-dimensional results, this paper establishes Jensen's inequality for partial traces within both semifinite and general non-tracial von Neumann algebras.
This paper provides a complete characterization of -positivity and Schmidt numbers for linear maps and bipartite states with symplectic group symmetries, yielding new constructions of optimal indecomposable maps, high-degree PPT entangled states, and resolutions to the PPT-squared conjecture and a Pal-Vertesi conjecture.
This paper investigates higher property T by providing new operator-algebraic characterizations and exploring its relationship with cohomological, rigidity, and geometric phenomena in lattices of semisimple Lie groups below their real rank, culminating in a unifying conjectural framework.
This paper establishes explicit formulas for a quantum invariant functor on projective varieties over number fields, with a detailed analysis of the specific case involving abelian varieties with complex multiplication.
This paper investigates the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms between groupoid and coarse-geometric models, demonstrating that strong phases are detected by position spectral triples while phases arising from stacking along Delone sets are inherently weak in the coarse-geometric sense.
This paper introduces a Fourier-type formalism on non-commutative spaces to establish two versions of the Hörmander-Mikhlin -multiplier theorem for locally compact Kac groups and semi-finite von Neumann algebras, which generalize classical results and are applied to evolution equations in non-commutative settings.
This paper investigates analogues of exactness for locally compact groupoids, proving that six natural definitions of exactness are equivalent for the class of inner amenable étale groupoids and highlighting the crucial role of exactness in understanding the relationship between groupoid amenability and the coincidence of full and reduced C*-algebras.
This paper establishes a measure-theoretic framework for constructing Arveson systems from stationary factorizing measure types, providing a rigorous characterization of spatiality and a robust mechanism for generating type III systems via infinite products, which is applied to derive explicit type III random-set systems from the zero sets of Brownian motion.
This paper characterizes positive surjective isometric Fourier multipliers on non-commutative -spaces of a locally compact group for , proving that such operators arise if and only if their symbols are locally almost everywhere equal to continuous characters of the group, thereby extending previous results from the unimodular to the general setting.
This paper demonstrates that under the condition of a tracially sequentially-split -homomorphism of order zero, key regularity properties including tracial -comparison, tracial -almost divisibility, and tracial nuclear dimension less than are preserved from a target unital -algebra to a source algebra .
This paper establishes a groupoid-equivariant formulation of the Fredholm index by constructing a natural KK-theory class for Fredholm operators within the unitary conjugation groupoid framework, demonstrating that its composition with the Calkin extension boundary map recovers the classical index.
This paper argues that the Gelfand–Naimark duality between compact Hausdorff spaces and unital commutative C*-algebras offers profound insights into the structure of compact Hausdorff spaces, particularly regarding Čech–Stone remainders and their autohomeomorphisms.
This paper establishes that an affine transformation in is a product of two coninvolutions if and only if its linear part is -reversible, while also characterizing products of three coninvolutions and proving that every transformation with a linear part of unit determinant is a product of at most four coninvolutions.
This paper explicitly computes the spectral metric, torsion, and Einstein tensors for a specific nontrivial spectral triple on a noncommutative torus, demonstrating that both the torsion and the Einstein tensor identically vanish.
This paper introduces an intrinsic deformation of smooth function algebras on compact Riemannian manifolds via spectral channel twisting, establishes conditions for its extension to Sobolev algebras and associativity, and demonstrates that classical strict deformations arising from abelian group actions are unified as specific instances of this framework.
This paper establishes a sharper upper bound for the amenability constant of the Fourier algebra of discrete groups and uses it to calculate explicit values for new classes of discrete and compact groups, thereby providing further evidence for the conjecture that Runde's lower bound is an equality.
This paper establishes a non-unitary version of the Bisognano-Wichmann property and proves Haag duality for nets of smeared Wightman fields by deriving Tomita-Takesaki-like results directly from Wightman axioms, thereby extending these fundamental algebraic quantum field theory concepts to non-unitary theories where traditional Hilbert space functional analysis tools are unavailable.