Related papers: Operator means, barycenters, and fixed point equat…
Using the properties of geometric mean, we shall show for any $0\le \alpha ,\beta \le 1$, \[f\left( A{{\nabla }_{\alpha }}B \right)\le f\left( \left( A{{\nabla }_{\alpha }}B \right){{\nabla }_{\beta }}A \right){{\sharp}_{\alpha }}f\left(…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
In this note, we consider a framework for the analysis of iterative algorithms which can described in terms of a structured set-valued operator. More precisely, at each point in the ambient space, we assume that the value of operator can be…
We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…
We introduce the notion of a coordinate $\mathbf{k}$-algebra scheme and the corresponding notion of a $\mathcal{B}$-operator. This class of operators includes endomorphisms and derivations of the Frobenius map, and it also generalizes the…
We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.
The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of many optimization algorithms. Firmly nonexpansive operators…
We introduce a new class of asymptotic contractions that employs two quasi-metrics defined directly in terms of the underlying mapping. The contraction condition compares these two quantities via a sequence of bounding functions that…
In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of…
The rational fixed point of a set functor is well-known to capture the behaviour of finite coalgebras. In this paper we consider functors on algebraic categories. For them the rational fixed point may no longer be fully abstract, i.e. a…
In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections…
This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…
In this work, we introduce the concept of $C^{*}$-algebra valued asymetric metric space, the concept of forward and the concept of backward $C^{*}$ valued asymetric contractions. We discuss the existence and uniqueness of fixed points for a…
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…