相关论文: Positivity of spectral shift functions and infinit…
The paper mainly deals with suprema and infima of self-adjoint operators in a von Neumann algebra $\mathcal{M}$ with respect to the spectral order. Let $\mathcal{M}_{sa}$ be the self-adjoint part of $\mathcal{M}$ and let $\preceq$ be the…
We introduce the concept of a \mu-scale invariant operator with respect to unitary transformation in a separable complex Hilbert space. We show that if a nonnegative densely defined symmetric operator is \mu-scale invariant for some \mu >0,…
We start with the Birman--Solomyak approach to define double operator integrals and consider applications in estimating operator differences $f(A)-f(B)$ for self-adjoint operators $A$ and $B$. We present the Birman--Solomyak approach to the…
For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…
This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of $\R^n$, with $n \geq 2$, we prove the stability of the first and zero order coefficients of…
In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the absolute continuity of spectral…
We study the asymptotic behavior as L \to \infty of the finite-volume spectral shift function for a positive, compactly-supported perturbation of a Schr\"odinger operator in d-dimensional Euclidean space, restricted to a cube of side length…
We study the trace class perturbations of the whole-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we refine the Lieb--Thirring…
In this paper, we consider positive Desch-Schappacher perturbations of bi-continuous semigroups on $\mathrm{AM}$-spaces with an additional property concerning the additional locally convex topology. As an examples, we discuss perturbations…
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
In this paper, we solve a spectral problem about positive semi-definite trace-class pseudodifferential operators on modulation spaces which was posed by H. Feichtinger. Later, C. Heil and D. Larson rephrased the problem in the broader…
We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre\u{\i}n type for a perturbation of an operator monotonic (negative complete Bernstein)…
We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant $J$-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation…
We provide criteria for self-adjointness and {\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A…
The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its…
In this paper I prove existence of an irreducible pair of operators $H$ and $H+V,$ where $H$ is a self-adjoint operator and $V$ is a self-adjoint trace-class operator, such that the singular spectral shift function of the pair is non-zero…
We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…
In \cite{Mor}, Marcantognini and Mor\'{a}n obtained Koplienko-Neidhardt trace formula for pairs of contractions and pairs of maximal dissipative operators via multiplicative path. In this article, we prove the existence of higher-order…
We prove sufficient conditions for Hausdorff convergence of the spectra of sequences of closed operators defined on varying Hilbert spaces and converging in norm-resolvent sense, i.e. $\|J_\varepsilon(1+A_\varepsilon)^{-1} -…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…