Related papers: An operadic approach to operator-valued free cumul…
Let $\mathbb{P}$ be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on $\mathbb{P}$,…
The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement…
A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field)…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
We employ the framework of operational calculus to derive the operators associated with the spherical mean and a class of related averaging means of a function in $n$-dimensional space. Beginning with the classical definition of the…
The construction of bases for quotients is an important problem. In this paper, applying the method of rewriting systems, we give a unified approach to construct sections---an alternative name for bases in semigroup theory---for quotients…
In this work, we make use of Lie algebraic methods to obtain the time evolution operator for an optomechanical system with linear and quadratic couplings between the field and the mechanical oscillator. Firstly, we consider the case of a…
We provide an operator space version of Maurey's factorization theorem. The main tool is an embedding result of independent interest. Applications for operator spaces and noncommutative Lp spaces are included.
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
We adopt an operatorial method based on the so-called creation, annihilation and number operators in the description of different systems in which two populations interact and move in a two-dimensional region. In particular, we discuss…
It has been shown by Voiculescu and Biane that the analytic subordination property holds for free additive and multiplicative convolutions. In this paper, we present an operatorial approach to subordination for free multiplicative…
A new hierarchy of operads over the linear spans of $\delta$-cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of the operad of permutations, also known as the associative symmetric operad.…
It is explained how the time evolution of the operadic variables may be introduced. As an example, a 2-dimensional binary operadic Lax representation of the harmonic oscillator is found.
Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some…