Related papers: Exposed positive maps in M_4(C)

The positive linear maps $\ad_s$ which send matrices $x$ to $s^*xs$ play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak [Linear Multilinear Alg. 61 (2013), 970--975] that the map $\ad_s$…

A natural and intrinsic characterization of the structure of the set $\mathfrak{C}$ of positive unital maps is given, i.e. it is shown that $\mathfrak{C}$ is isometrically isomorphic to the subset $\gD$ of bp-positive density matrices…

We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.

We exhibit infinite families of planar graphs with real chromatic roots arbitrarily close to 4, thus resolving a long-standing conjecture in the affirmative.

It is known that every hereditary property can be characterized by finitely many minimal obstructions when restricted to either the class of cographs or the class of $P_4$-reducible graphs. In this work, we prove that also when restricted…

We describe convex quadric surfaces in n dimensions and characterize them as convex surfaces with quadric sections by a continuous family of hyperplanes.

We identify a family of $O(|E(G)|^2)$ nontrivial facets of the connected matching polytope of a graph $G$, that is, the convex hull of incidence vectors of matchings in $G$ whose covered vertices induce a connected subgraph. Accompanying…

We study the projective special Kaehler condition on groups, providing an intrinsic definition of homogeneous projective special Kaehler that includes the previously known examples. We give intrinsic defining equations that may be used…

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…

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…

Let $D$ be a space of $2\times n$ matrices. Then the face of the cone of all completely positive maps from $M_2$ into $M_n$ given by $D$ is an exposed face of the bigger cone of all decomposable positive linear maps if and only if the set…

We show that each positive map from B(K) to B(H) with K and H finite dimensional Hilbert spaces is a scalar multiple of a map of the form $Tr - \psi$ with $\psi$ completely positive. This is used to give necessary and sufficient conditions…

We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still…

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied…

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

We give conditions for when the tensor product of two positive maps between matrix algebras is a positive map. This happens when one map belongs to a symmetric mapping cone and the other to the dual cone. Necessary and sufficient conditions…

4-critical wheel graphs of higher order are considered concerning their belonging to free-planar or free-Hadwiger classes.

In this article, we introduce a new family of sense preserving harmonic mappings f in the open unit disk and prove that functions in this family are close-to-convex. We give some basic properties such as coefficient bounds, growth…

We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once-punctured polygons which, in turn, contain all possible geometric flip-graphs of…

Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open…