Related papers: Perturbations and operator trace functions

We obtain Taylor approximations for functionals $V\mapsto Tr(f(H_0+V))$ defined on the bounded self-adjoint operators, where $H_0$ is a self-adjoint operator with compact resolvent and $f$ is a sufficiently nice scalar function, relaxing…

This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by applications in scattering theory, we consider both trace-class…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…

Our goal is to extend the theory of the spectral shift function to the case where only the difference of some powers of the resolvents of self-adjoint operators belongs to the trace class. As an example, we consider a couple of Dirac…

In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…

In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the Hilbert-Schmidt class $\mathcal{S}^2(\mathcal{H})$ by…

Gramsch and Lay [10] gave spectral mapping theorems for the Dunford-Taylor calculus of a closed linear operator $T$, $$\widetilde{\sigma}_i(f(T)) = f(\widetilde{\sigma}_i(T)), $$ for several extended essential spectra…

We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…

Let $f:{\mathbb R}_+\mapsto {\mathbb R}$ be a smooth function with $f(0)=0.$ A problem of estimation of a functional $\tau_f(\Sigma):= {\rm tr}(f(\Sigma))$ of unknown covariance operator $\Sigma$ in a separable Hilbert space ${\mathbb H}$…

Let A and E be Hermitian self-adjoint matrices, where A is fixed and E a small perturbation. We study how the eigenvalues and eigenvectors of A+E depend on E, with the aim of obtaining first order formulas (and when possible also second…

This is a report on a joint work [12] with D. Essouabri, C. Levy and A. Sitarz. The spectral action on noncommutative torus is obtained, using a Chamseddine--Connes formula via computations of zeta functions. The importance of a Diophantine…

The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-adjoint and maximal dissipative operators. They cover both…

We study the Spectral Analysis for a class of bounded linear operators T = D + F in a non Archimedean Hilbert space E, where D is a diagonal linear operator and where F is a finite rank linear operator. In this study of the Spectral…

We establish estimates and representations for the remainders of Taylor approximations of the spectral action functional $V\mapsto\tau(f(H_0+V))$ on bounded self-adjoint perturbations, where $H_0$ is a self-adjoint operator with…

We push the definition of multiple operator integrals (MOIs) into the realm of unbounded operators, using the pseudodifferential calculus from the works of Connes and Moscovici, Higson, and Guillemin. This in particular provides a natural…

We establish higher order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator…

In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.

Trace formulas appear in many forms in noncommutative geometry (NCG). In the first part of this thesis, we obtain results for asymptotic expansions of trace formulas like heat trace expansions by adapting the theory of Multiple Operator…

We review previous work on spectral flow in connection with certain self-adjoint model operators $\{A(t)\}_{t\in \mathbb{R}}$ on a Hilbert space $\mathcal{H}$, joining endpoints $A_\pm$, and the index of the operator $D_{A}^{}= (d/d t) + A$…