Related papers: $C^\ast$-extreme maps and nests

In this paper we generalize a specific quantized convexity structure of the generalized state space of a $C^*$-algebra and examine the associated extreme points. We introduce the notion of $P$-$C^*$-convex subsets, where $P$ is any positive…

In this work, we study a sub-collection of unital completely positive maps from a unital $C^\ast$-algebra $\mathcal{A}$ to $\mathcal{B}(\mathcal{H})$, the algebra of bounded linear operators on a Hilbert space $\mathcal{H}$ in the setting…

In this paper, we investigate the general properties and structure of $C^*$-extreme points within the $C^*$-convex set $\mathrm{UCP}(\mathcal{A},B(\mathcal{H}))$ of all unital completely positive (UCP) maps from a unital real $C^*$-algebra…

The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative…

We consider the convex set of ( unital ) positive ( completely ) maps from a $C^*$ algebra $\cla$ to a von-Neumann sub-algebra $\clm$ of $\clb(\clh)$, the algebra of bounded linear operators on a Hilbert space $\clh$ and study its extreme…

The purpose of this short note is to clarify and present a general version of an interesting observation by Piani and Mora (Physic. Rev. A 75, 012305 (2007)), linking complete positivity of linear maps on matrix algebras to decomposability…

Let $\mathcal E$ denote the set of all unital entanglement breaking (UEB) linear maps defined on an operator system $\mathcal S \subset M_d$ and, mapping into $M_n$. As it turns out, the set $\mathcal E$ is not only convex in the classical…

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use…

In this paper we study the $C^*$-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of $C^*$-extreme points are discussed. By establishing a Radon-Nikodym type…

We prove lifting theorems for completely positive maps going out of exact $C^\ast$-algebras, where we remain in control of which ideals are mapped into which. A consequence is, that if $\mathsf X$ is a second countable topological space,…

We say that a unital C*-algrebra A has the approximate positive factorization property (APFP) if every element of A is a norm limit of products of positive elements of A. (There is also a definition for the nonunital case.) T. Quinn has…

This article studies generalizations of (matrix) convexity, including partial convexity and biconvexity, under the umbrella of $\Gamma$-convexity. Here $\Gamma$ is a tuple of free symmetric polynomials determining the geometry of a…

The classical Choquet theorem establishes a barycentric decomposition for elements in a compact convex subset of a locally convex topological vector space. This decomposition is achieved through a probability measure that is supported on…

We give necessary and sufficient conditions which a graph should satisfy in order for its associated $C^\ast$-algebra to have a $T_1$ primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are…

We introduce and study a class $\mathcal{M}$ of generalized positive definite kernels of the form $K\colon X\times X\to L(\mathfrak{A},L(H))$, where $\mathfrak{A}$ is a unital $C^{*}$-algebra and $H$ a Hilbert space. These kernels encode…

We find a description of the restriction of doubly stochastic maps to separable abelian $C^*$-subalgebras of a II$_1$ factor $\cM$. We use this local form of doubly stochastic maps to develop a notion of joint majorization between…

Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…

In this article, we introduce and investigate a class of C$^{\ast}$-algebras generated by reduced graph products of C$^{\ast}$-algebras, augmented with families of projections naturally associated with words in right-angled Coxeter groups.…

We propose two interrelated advances in the theory of adjointable operators on Hilbert C*-modules. First, we give a set of equivalent, verifiable conditions characterizing positivity of general $n\times n$ block operator matrices acting on…

Let n be a positive integer and c an n-tuple of natural numbers. A convex set in Euclidean n-space given by a family of linear relations in the elements of c and depending on their natural order is defined. The extremal elements of this…