相关论文: Vigier's theorem for the spectral order and its ap…

In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.

For a {bounded} non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space H and possessing a dense range R we propose a new approach to characterisation of phenomenon concerning the existence of…

Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…

We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on $[a,\infty)$, $a\in\mathbb{R}$, with a regular finite end point $a$ and the case of Schr\"odinger…

This chapter deals with the notion of the resolvent of a self-adjoint operator. We pay special attention to the convergence of unbounded self-adjoint operators in several resolvent senses, and how they are related to the convergence of…

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…

Given an infinite graph $G$ on countably many vertices, and a closed, infinite set $\Lambda$ of real numbers, we prove the existence of an unbounded self-adjoint operator whose graph is $G$ and whose spectrum is $\Lambda$.

The "Up-and-down" theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result of the operator theory. We prove an analog of this theorem for a positive abstract Uryson…

Let $\mathfrak{M}$ be a von Neumann algebra and let $A$ be a nonzero positive element of $\mathfrak{M}$. By $\sigma_A(T) $ and $r_A(T)$ we denote the $A$-spectrum and the $A$-spectral radius of $T\in\mathfrak{M}^A$, respectively. In this…

A new geometric proof of the spectral theorem for unbounded self-adjoint operators A in a Hilbert space H is given based on a splitting of A in positive and negative parts A+ and A-. For both operators A+ and A- the spectral family can be…

We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…

Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the…

We revisit Haagerup's enigmatic reduction theorem \cite[Theorems 2.1 \& 3.1]{HJX} showing how that theorem may be extended to general von Neumann algebras $\M$ equipped with an arbitrary faithful normal semifinite weight in a manner which…

Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this…

John von Neumann's spectral theorem for self-adjoint operators is a cornerstone of quantum mechanics. Among other things, it also provides a connection between expectation values of self-adjoint operators and expected values of real-valued…

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…

In this paper, we will prove a spectral theorem for self-adjoint compactoid operators. Also, we will study the condition on which the coefficient field must be imposed. In order to get the theorems, we will use the Fredholm theory for…

This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…

We obtain a solution to the Bessis-Moussa-Villani conjecture for a trace-class perturbation of a semi-bounded operator and answer affirmatively the question on positivity of higher order spectral shift functions in the setting of…

We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and…