Related papers: Perturbations and operator trace functions

In this paper we study spectral function for a nonsymmetric differential operator on the half line. Two cases of the coefficient matrix are considered, and for each case we prove by Marchenko's method that, to the boundary value problem,…

We consider an algebra $\mathscr A$ of Fourier integral operators on $\mathbb R^n$. It consists of all operators $D: \mathscr S(\mathbb R^n)\to \mathscr S(\mathbb R^n)$ on the Schwartz space $\mathscr S(\mathbb R^n)$ that can be written as…

We extend the multiplicative submodularity of the principal determinants of a nonnegative definite hermitian matrix to other spectral functions. We show that if $f$ is the primitive of a function that is operator monotone on an interval…

By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…

Let f be a function defined on positive numbers. The subject is the trace inequality $Tr f(A) + Tr f(P_2AP_2) \le Tr f(P_{12}AP_{12}) + \Tr f(P_{23}AP_{23})$, where $A$ is a positive operator, $P_1,P_2,P_3$ are orthogonal projections such…

In this study, we define discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Gr\"unwald-Letnikov fractional operators with both delta and nabla operators. We show selfadjointness of the DFSL operator for the…

We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…

In the context of A. Connes' spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. A. Connes' construction of spectral triples for group algebras…

For any densely defined, lower semi-continuous trace \tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2,…

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…

Let $A$ be a $\nu$-vector of self-adjoint, pairwise commuting operators and $B$ a bounded operator of class $C^{n_0}(A)$. We prove a Taylor-like expansion of the commutator $[B,f(A)]$ for a large class of functions $f\colon\mathbm{R}^\nu…

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $\mathcal D(T)$. Assume that the spectrum of $T$ is confined in the union of disjoint intervals $\Delta_k =[\alpha_{2k-1},\alpha_{2k}]$, $k\in \mathbb{Z}$, and $$…

We construct an analogue of Kontsevich and Vishik's canonical trace for a class of pseudodifferential boundary value problems in Boutet de Monvel's calculus on compact manifolds with boundary. For an operator A in the calculus (of class…

We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a…

We study singular Sturm-Liouville operators of the form \[ \frac{1}{r_j}\left(-\frac{\mathrm d}{\mathrm dx}p_j\frac{\mathrm d}{\mathrm dx}+q_j\right),\qquad j=0,1, \] in $L^2((a,b);r_j)$, where, in contrast to the usual assumptions, the…

We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…

We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…

Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral…

We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let $A$ and $V$ be bounded self-adjoint operators. Assume that the spectrum of $A$ consists of two disjoint parts…

We introduce the non-commutative $f$-divergence functional $\Theta(\widetilde{A},\widetilde{B}):=\int_TB_t^{\frac{1}{2}}f\left(B_t^{-\frac{1}{2}} A_tB_t^{-\frac{1}{2}}\right)B_t^{\frac{1}{2}}d\mu(t)$ for an operator convex function $f$,…