Related papers: Exact and approximate operator parallelism

Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.

This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…

Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…

multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…

In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that -- is a frame for H, for some -- . We state a necessary condition in order for a frame -- to have a…

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given a positive operator $A\in\B(\h)$, and a number $\lambda\in [0,1]$, a…

In the theory of Hilbert $C^*$-modules over a $C^*$-algebra $A$ (in contrast with the theory of Hilbert spaces) not each bounded operator ($A$-homomorphism) admits an adjoint. The interplay between the sets of adjointable and…

We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint…

We study the question when for a given *-algebra $\mathcal{A}$ a sequence of cones $C_n\in M_n(\mathcal{A})$ can be realized as cones of positive operators in a faithful *-representation of $\mathcal{A}$ on a Hilbert space. A…

We initiate an investigation into how much the existing theory of (nonselfadjoint) operator algebras on a Hilbert space generalizes to algebras acting on L^p spaces. In particular we investigate the applicability of the theory of real…

We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…

The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as n-quasi-m-isometric operators acting on an infinite complex separable Hilbert space H. This generalizes the class of m-isometric…

This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental…

Cauchy problem for an abstract hyperbolic equation with the Lipschitz continuous operator is considered in the Hilbert space. The operator corresponding to the elliptic part of the equation is a sum of operators…

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…

Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…

Let $\mathscr{H}$ be a complex Hilbert space, and let $\mathscr{B}(\mathscr{H})$ denote the set of all bounded operators on $\mathscr{H}$ . For an operator $T \in \mathscr{B}(\mathscr{H})$, let $|T| := (T^*T)^{\frac{1}{2}}$. For $A$ in…

Let $\mathcal{H}$ be a separable infinite-dimensional complex Hilbert space and let $\mathcal{J}$ be a two-sided ideal of the algebra of bounded operators $\mathcal{B}(\mathcal{H})$. The groups $\mathcal{G} \ell_\mathcal{J}$ and…

We consider random linear continuous operators $\Omega \to \mathcal{L}(\mathcal{H}, \mathcal{H})$ on a Hilbert space $\mathcal{H}$. For example, such random operators may be random quantum channels. The Central Limit Theorem is known for…

An adjoint pair is a pair of densely defined linear operators $A, B$ on a Hilbert space such that $\langle Ax,y\rangle=\langle x,By\rangle$ for $x\in \cD(A), y \in \cD(B).$ We consider adjoint pairs for which $0$ is a regular point for both…