Related papers: Experiments with a Positivity Preserving Operator

We show that the symmetrized product $AB+BA$ of two positive operators $A$ and $B$ is positive if and only if $f(A+B)\leq f(A)+f(B)$ for all non-negative operator monotone functions $f$ on $[0,\infty)$ and deduce an operator inequality. We…

Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of…

Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…

Let \(\mathcal{A}\) be a finite-dimensional real (or complex) C*-algebra, \(\Omega_{A}\) an aperiodic subshift of finite type, and \(\mathcal{C}(\Omega_{A}; \mathcal{A})\) the set of continuous functions from \(\Omega_{A}\) to…

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…

In this review paper, we explore operator aspects in extremal properties of Bernstein-type polynomial inequalities. We shall also see that a linear operator which send polynomials to polynomials and have zero-preserving property naturally…

In this paper we consider the cone of all positive, bounded operators acting on an infinite dimensional, complex Hilbert space, and examine bijective maps that preserve absolute continuity in both directions. It turns out that these maps…

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…

In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…

Let $\sigma$ be a non-trivial operator mean in the sense of Kubo and Ando, and let $OM_+^1$ the set of normalized positive operator monotone functions on $(0, \infty)$. In this paper, we study class of $\sigma$-subpreserving functions $f\in…

The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with…

We study a positivity preservation property for Schr\"odinger operators with singular potential on geodesically complete Riemannian manifolds with non-negative Ricci curvature. We apply this property to the question of self-adjointness of…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

We consider the third order operator with small 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers all real line. Under the minimal conditions on the coefficients we show that there…

Given a topological group $G$ and a unitary representation $U$ of $G$, we consider the problem of classifying the positive operator measures which are based on a $G$-homogeneous space $X$ and covariant with respect to the representation…

We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…

We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…

This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical…