Related papers: Real decomposable maps on operator systems

We show that a map between projection lattices of semi-finite von Neumann algebras can be extended to a Jordan $*$-homomorphism between the von Neumann algebras if this map is defined in terms of the support projections of images (under the…

We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

We propose the notion of countable decomposability of maps on C*-algebras: a bounded linear map $\varphi : \mathscr{A}\to B(\mathcal{H})$, where $\mathscr{A}$ is a C*-algebra and $\mathcal{H}$ a Hilbert space, will be called countably…

We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…

In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.

Most of this article is an expanded version of our conference talk. It is essentially a survey, but some part, like most of the lengthy Section 5, is comprised of new results whose proofs are unpublished elsewhere. We begin by reviewing the…

The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive…

We introduce a new and extensive theory of noncommutative convexity along with a corresponding theory of noncommutative functions. We establish noncommutative analogues of the fundamental results from classical convexity theory, and apply…

Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if (W*(x)' cap M) unitally contains a factor of type I_n. We decide the density of the n-divisible operators, for various n,…

We verify that a large portion of the theory of complex operator spaces and operator algebras (as represented by the 2004 book by the author and Le Merdy for specificity) transfers to the real case. We point out some of the results that do…

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…

A construction of reversible extensions of dynamical systems which applies to arbitrary mappings (not necessarily with open range) is presented. It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to…

The problem of classification of decomposable (in the sense of Stormer) positive maps between matrix algebras is presented. We propose the new notion of "finite" version of decomposability ($k$-decomposabilty). The characterisation of…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan…

Nuclear C*-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in…

Representations of Hom-Jacobi-Jordan algebras are studied. In particular, adjoint representations and trivial representations are studied in detail. Derivations and central extensions of Hom-Jacobi-Jordan algebras are also discussed as an…

We establish the dual equivalence of the category of (potentially nonunital) operator systems and the category of pointed compact nc (noncommutative) convex sets, extending a result of Davidson and the first author. We then apply this dual…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification…