Related papers: Extremal positive maps on $M_{3}(\mathbb{C})$ and …
Idempotent analogues of convexity are introduced. It is proved that the category of algebras for the capacity monad in the category of compacta is isomorphic to the category of $(\max,\min)$-idempotent biconvex compacta and their biaffine…
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators…
We present three equivalence classes of rational non-invertible multidimensional compatible maps. These maps turns out to be idempotent and by construction they admit birational partial inverses (companion maps) which are Yang-Baxter maps.…
Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory.…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be \textit{idempotent compressible} if $E\mathcal{A}E$ is an algebra for all idempotents $E\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be…
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…
Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
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…
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…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…
In this paper we consider the unbounded local completely positive and local completely contractive maps on maximal tensor product of unital locally C*-algebras and discuss on extremal points of certain convex subsets in the set of such…
We construct a new class of positive indecomposable maps in the algebra of 'd x d' complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d=3. It provides a new reach…
Let $\Gamma$ be a finitely generated group of matrices over $\mathbb{C}$. We construct an isometric action of $\Gamma$ on a complete CAT(0) space $X$ such that the restriction of this action to any subgroup of $\Gamma$ containing no…
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…
This article proves the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive reflection groups to the set of bounded operators, and uses those linear maps to define creation and annihilation…