Related papers: Unbounded operators having self-adjoint or normal …

A classical theorem of von Neumann asserts that every unbounded self-adjoint operator $A$ in a separable Hilbert space $H$ is unitarily equivalent to an operator $B$ in $H$ such that $D(A)\cap D(B)=\{0\}$. Equivalently this can be…

We study the threshold behaviour of two dimensional Schr{\" o}dinger operators with finitely many local point interactions. We show that the resolvent can either be continuously extended up to the threshold, in which case we say that the…

We study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces $A^p(\Omega),$ $1<p<\infty,$ where $\Omega\subset \mathbb{C}$ is a bounded simply connected domain with polygonal boundary. We give sufficient…

Following Berm\'udez et al. (ArXiv: 1706.03638v1), we study the rate of growth of the norms of the powers of a linear operator, under various resolvent conditions or Ces\`aro boundedness assumptions. We show that $T$ is power-bounded if…

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…

For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…

We study the adjointness problem for the closed extensions of a general b-elliptic operator A in x^{-\nu}Diff^m_b(M;E), \nu>0, initially defined as an unbounded operator A:C_c^\infty(M;E)\subset x^\mu L^2_b(M;E)\to x^\mu L^2_b(M;E), \mu \in…

We apply G-convergence theory to study the asymptotic of the eigenvalue problems of positive definite bounded self-adjoint $h$-dependent operators as $h\to\infty$. Two operators are considered; a second order elliptic operator and a general…

Given two linear operators $S$ and $T$ acting between Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$, respectively $\mathscr{K}$ and $\mathscr{H}$ which satisfy the relation \begin{equation*} \langle Sh, k\rangle=\langle h, Tk\rangle, \quad…

In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a…

We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These bounds are applied to obtain new results on the distribution of…

The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any…

In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair consists of two densely defined linear operators $A$ and…

Building on results of Haagerup and Schultz, we decompose an arbitrary operator in a diffuse, finite von Neumann algebra into the sum of a normal operator and an s.o.t.-quasinilpotent operator. We also prove an analogue of Weyl's inequality…

Our goal is to compare various results for Toeplitz $T$ and Hankel $H$ operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define…

We construct a formally self-adjoint Hamiltonian whose eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. We consider a two-dimensional Hamiltonian which couples the Berry-Keating Hamiltonian to the number operator…

We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which,…

We consider a quasinilpotent operator whose resolvent is entire operator function of exponential type. Let A be its one-dimensional perturbation. We establish necessity of Muckenhoupt condition (A2) for two weights related to operator A for…

Given a power-bounded linear operator T in a Banach space and a probability F on the non-negative integers, one can form a `subordinated' operator S = \sum_k F(k) T^k. We obtain asymptotic properties of the subordinated discrete semigroup…

It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous…