Related papers: On von Neumann spectral triples

We investigate the relations between the (completely bounded) local Coulhon-Varopoulos dimension and the spectral dimension of spectral triples associated to sub-Markovian semigroups (or Dirichlet forms) acting on classical (or…

The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…

We study characteristic classes on hyperk\"ahler manifolds with a view towards the Verbitsky component. The case of the second Chern class leads to a conditional upper bound on the second Betti number in terms of the Riemann--Roch…

We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic $K$-theoretic invariants…

We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As…

The paper is devoted to the description of $2$-local derivations on von Neumann algebras. Earlier it was proved that every $2$-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of…

We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. The algebra, which is assumed to be…

To describe external and internal attributes of fundamental fermions, a theory of multi-spinor fields is developed on an algebra, a {\it triplet algebra}, which consists of all the triple-direct-products of Dirac \gamma-matrices. The…

We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…

It is shown that the *-algebra of all (closed densely defined linear) operators affiliated with a finite type I von Neumann algebra admits a unique center-valued trace, which turns out to be, in a sense, normal. It is also demonstrated that…

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, for the Lefschetz number of D as the…

Continuing previous work we develop a certain piece of functional analysis on general graphs and use it to create what Connes calls a 'spectral triple', i.e. a Hilbert space structure, a representation of a certain (function) algebra and a…

We pursue Arthur's invariant trace formula for certain coverings of connected reductive groups by deducing explicit formulas for its spectral side. This is based on some results in local harmonic analysis from an earlier preprint. The…

We take the trace of Von-Neumann's ergodic theorem and get a trace formula of a unitary matrix family. It is an extension of Poisson summation formula in higher dimension. We also construct a family of crystalline measure with complex…

We experiment with some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We look at matrices defined by Gaussian primes and look at the growth of the…

In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt…

We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral triple in the sense of Connes, is obtained from it. The…

We consider the spectral behavior and noncommutative geometry of commutators $[P,f]$, where $P$ is an operator of order $0$ with geometric origin and $f$ a multiplication operator by a function. When $f$ is H\"{o}lder continuous, the…

Among ideals of compact operators on a Hilbert space we identify a subclass of those closed with respect to the logarithmic submajorization. Within this subclass, we answer the questions asked by Pietsch \cite{Pietsch_nachrichten} and by…