Related papers: Perturbation formulas for traces on normed ideals

We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator on $\mathbb{R}^{n}$ whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to…

Based on a previous paper [Chr17] on Neumann data for Dirichlet eigenfunctions on triangles, we extend the study in two ways. First, we investigate the (semi-classical) Neumann data mass on perturbed triangles. Specifically, we replace one…

In [10], Halmos proved an interesting result that the set of irreducible operators is dense in $\mathcal B(\mathcal H)$ in the sense of Hilbert-Schmidt approximation. In a von Neumann algebra $\mathcal M$ with separable predual, an operator…

Let $\M$ be a type ${\rm II_1}$ factor and let $\tau$ be the faithful normal tracial state on $\M$. In this paper, we prove that given finite elements $X_1,\cdots X_n \in \M$, there is a finite decomposition of the identity into $N \in…

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…

By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and Gaussian noise. Using an integral representation of the evolution operator we investigate the high order corrections to the…

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large…

Dual quaternion matrices have important applications in multi-agent formation control. In this paper, we first address the concept of spectral norm of dual quaternion matrices. Then, we introduce a von Neumann type trace inequality and a…

We consider discontinuous perturbations of smooth endomorphisms and show that if the perturbed family satisfies uniform mixing assumptions on standard pairs the physical measure is Lipschitz in the parameter defying the perturbation. We…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded semidefinite perturbation is considered. A variant of the Davis-Kahan $ \sin2\Theta $ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46]…

Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$…

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…

The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…

The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we…

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 this paper, the regularized trace formulas for a diffusion operator which include conformable fractional derivatives of order {\alpha} (0<{\alpha \leq 1}) is obtained.

Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…