Related papers: Operator means deformed by a fixed point method

This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the properties of the inverse of the related pentadiagonal matrices, associated with the fourth-order nonlinear beam equation. This nonlinear problem is…

A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…

This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operator is compressed along a chosen unit vector while remaining…

We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…

Let~$X=\Po/\Gamma$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(\Gamma)$ based on the classical theory of uniformizing differential equations and accessory…

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…

Let $T$ be a bounded linear operator on a Hilbert space $\mathcal{H}$, and let $T \equiv V|T|$ be the polar decomposition of $T$. The mean transform of $T$ is defined by $\widehat{T}:=\frac{1}{2}(V|T|+|T|V)$. In this paper we study the…

This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming…

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…

We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…

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…

We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…

The operator monotone functions defined in the positive half-line are of particular importance. We give a version of the theory in which integral representations for these functions can be established directly without invoking L\"owner's…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…

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…

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.