Related papers: On the positive fixed points of quartic operators

We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contractions. We classify all commuting unitary representations over…

We introduce and study a new class of nonlinear monotone operators acting in normal cones of real Banach spaces and possessing the property of strong concavity. We establish new constructive principles for the existence of nonzero fixed…

It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…

For two classes of bisexual populations we give a constructive description of quadratic stochastic operators which act to the Cartesian product of standard simplexes. We consider a bisexual population such that the set of females can be…

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.

We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give a geometric property of the spectral geometric mean as a…

In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.

In this paper we are going to prove a very general fixed point theorem for mappings acting in partial metric spaces. In that theorem we impose some conditions on behavior of considered mappings on orbits and a condition relating orbits of…

In the renormalisation analysis of critical phenomena in quasi-periodic systems, a fundamental role is often played by fixed points of functional recurrences of the form \begin{equation*} f_{n}(x) = \sum_{i=1}^\ell a_i(x) f_{n_i}…

Given a unitary representation $U$ of an Abelian group $G$ and a subgroup $H$, we characterise the positive operator valued quotient group $G/H$ and covariant with respect to $U$.

Consider a $C_0$-semigroup $(e^{tA})_{t \ge 0}$ on a function space or, more generally, on a Banach lattice $E$. We prove a sufficient criterion for the operators $e^{tA}$ to be positive for all sufficiently large times $t$, while the…

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 characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.

For a class of semilinear elliptic equations, we establish criteria that guarantee that the linearized operator associated with a solution satisfies certain spectral assumptions that are widely used in the analysis of the stability of…

We establish pointwise estimates for the ground states of some classes of posi- tivity preserving operators. The considered operators are negatively perturbed (by measures) strongly local Dirichlet operators. These estimates will be written…

We show that the quadratic matrix equation $VW + \eta (W)W = I$, for given $V$ with positive real part and given analytic mapping $\eta$ with some positivity preserving properties, has exactly one solution $W$ with positive real part. We…

In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.

In this article we prove results on logaritmic convexity of fixed points of stochastic kernel operators. These results are expected to play a key role in the economic application to strategic market games.

We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive $C_0$-semigroup on an $L^p$-space is strongly convergent in case that it has a strictly positive fixed point and contains an integral…

Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…