Related papers: Positivity, Betweenness and Strictness of Operator…
In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…
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 an operator monotone function $f(t)$ on the positive real line, we show the operator monotonicity of the type of the functions $(t-a)(t-b)/(f(t)-f(a))(f^\sharp(t)-f^\sharp(b))$.
A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…
We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…
We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables…
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…
In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions.…
The B-operators (abbreviation for Brownian-type operators) are upper triangular 2x2 block matrix operators that satisfy certain algebraic constraints. The purpose of this paper is to characterize the weak, the strongand the uniform…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
In this paper, the notion of operator means in the setting of JB-algebras is introduced and their properties are studied. Many identities and inequalities are established, most of them have origins from operators on Hilbert space but they…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
In this paper we present some characterizations for quasi-arithmetic operator means (among them the arithmetic and harmonic means) on the positive definite cone of the full algebra of Hilbert space operators, and also for the Kubo-Ando…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
Bisimulation metric is a robust behavioural semantics for probabilistic processes. Given any SOS specification of probabilistic processes, we provide a method to compute for each operator of the language its respective metric…
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…