Related papers: Spectral flow for nonunital spectral triples

We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic gauge configurations. We study both the unimproved and the HISQ Dirac operators. We compare the spectral flow index with the…

We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.

We show that the following conditions on a C*-algebra are equivalent: (i) it has the fixed point property for nonexpansive mappings, (ii) the spectrum of every self adjoint element is finite, (iii) it is finite dimensional. We prove that…

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

We introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the scattered radical. Among applications we find some sufficient…

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and…

This paper begins a new approach to the $r$-trace formula, without removing the nontempered contribution to the spectral side. We first establish an invariant trace formula whose discrete spectral terms are weighted by automorphic…

The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have…

Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the…

We define spectral freeness for actions of discrete groups on C*-algebras. We relate spectral freeness to other freeness conditions; an example result is that for an action of a finite group, spectral freeness is equivalent to strong…

We prove an abstract index formula about Sinnott's symbol between two different lattices. We also develop the theory of the universal distribution and predistribution in a double complex point of view. The theory of spectral sequence is…

In this second part of the paper, we define spectral spacetimes, a noncommutative generalization of Lorentzian orientable spacetimes of even dimension with a spin structure. There are two main differences with spectral triples: the…

An unsplittable multiflow routes the demand of each commodity along a single path from its source to its sink node. As our main result, we prove that in series-parallel digraphs, any given multiflow can be expressed as a convex combination…

In this note the notions of trace compatible operators and infinitesimal spectral flow are introduced. We define the spectral shift function as the integral of infinitesimal spectral flow. It is proved that the spectral shift function thus…

We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e.…

We consider a class of biased random walks on infinite graphs and present several general results on the spectral radius of biased random walk.

We offer a short proof of Connes' Hochschild class of the Chern character formula for non-unital semifinite spectral triples. The proof is simple due to its reliance on the authors' extensive work on a refined version of the local index…

We study the numerical differentiation formulae for functions given in grids with arbitrary number of nodes. We investigate the case of the infinite number of points in the formulae for the calculation of the first and the second…

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…