Related papers: Perspectives and completely positive maps
The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean,…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…
We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The theory is accomplished by introducing a new set-valued…
For a class of linear maps on a von Neumann factor, we associate two objects, bounded operators and trace class operators, both of which play the roles of Choi matrices. Each of them is positive if and only if the original map on the factor…
By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…
In a previous work by the authors the one dimensional (doubling) renormalization operator was extended to the case of quasi-periodically forced one dimensional maps. The theory was used to explain different self-similarity and universality…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
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 present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported…
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full operator algebra is normal. We also characterize those…
Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability…
We give an overview of certain aspects of tractability analysis of multivariate problems. This paper is not intended to give a complete account of the subject, but provides an insight into how the theory works for particular types of…
Recently, P\'{a}lfia introduced a generalized Karcher mean as a solution of an operator equation. In this article, we present several relations for this new mean. In particular, we investigate the behavior of this generalized mean when…
We prove that for two-component maps in dimension two, rank-one convexity is equivalent to quasiconvexity. The essential tool for the proof is a fixed-point argument for a suitable set-valued map going from one component to the other that…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
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…