Related papers: An Interpolation Problem for Completely Positive M…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
In this paper we study nonlinear interpolation problems for interpolation and peak-interpolation sets of function algebras. The subject goes back to the classical Rudin-Carleson interpolation theorem. In particular, we prove the following…
We characterise absolutely dilatable completely positive maps on the space of all bounded operators on a Hilbert space that are also bimodular over a given von Neumann algebra as rotations by a suitable unitary on a larger Hilbert space…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…
We develop a theory of partially defined complete positivity preservers, extending Schoenberg's classical characterization to functions defined only on discrete subsets or constrained domains. We frame the extension problem through the…
This chapter investigates the cone of copositive matrices, with a focus on the design and analysis of conic inner approximations for it. These approximations are based on various sufficient conditions for matrix copositivity, relying on…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…
We initiate a study of linear maps on $M_n(\mathbb{C})$ that have the property that they factor through a tracial von Neumann algebra $(\mathcal{A,\tau})$ via operators $Z\in M_n(\mathcal{A})$ whose entries consist of positive elements from…
Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…
A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…
We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and…
A new method of analysing positive bistochastic maps on the algebra of complex matrices $M_{3}$ has been proposed. By identifying the set of such maps with a convex set of linear operators on $\mathbb{R}^{8}$, one can employ techniques from…
The problem of polynomial least squares fitting in the standard Lagrange basis is addressed in this work. Although the matrices involved in the corresponding overdetermined linear systems are not totally positive, rectangular totally…
Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…