Related papers: Ordered group-valued probability, positive operato…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
We consider mixed powerdomains combining ordinary nondeterminism and probabilistic nondeterminism. We characterise them as free algebras for suitable (in)equation-al theories; we establish functional representation theorems; and we show…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
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…
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
We introduce a two-sorted algebraic theory whose models are states of MV-algebras and, to within a categorical equivalence that extends Mundici's well-known one, states of Abelian lattice-groups with (strong order) unit. We discuss free…
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
The common in ring, module and algebra is that they are Abelian group with respect to addition. This property is enough to study integration. I treat integral of measurable map into normed Abelian $\Omega$-group. Theory of integration of…
In this paper, we discuss positive maps induced by (irreducibly) covariant linear operators for finite groups. The application of group theory methods allows deriving some new results of a different kind. In particular, a family of…
In this work, we investigate the existence of a factorization for a unital completely positive map, between non-commutative probability space which do not change the expectation values of the events. These maps are called in literature…
In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the…
Given a K\"ahler manifold $(Z,J,\omega)$ and a compact real submanifold $M\subset Z$, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group ${\rm G}$ on the space of probability…
We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables; with…