Related papers: Inductive limits in the operator system and relate…
We use induction and interpolation techniques to prove that a composition operator induced by a map $\phi$ is bounded on the weighted Bergman space $\A^2_\alpha(\mathbb{H})$ of the right half-plane if and only if $\phi$ fixes $\infty$…
We define $\Delta$-equivalence for operator systems and show that it is identical to stable isomorphism. We define $\Delta$-contexts and bihomomorphism contexts and show that two operator systems are $\Delta$-equivalent if and only if they…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
Non-commutative multivariable versions of weighted shift operators arise naturally as `weighted' left creation operators acting on the Fock space Hilbert space. We identify a natural notion of periodicity for these $N$-tuples, and then find…
We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator…
Motivated by the recent interest in the examination of unital completely positive maps and their effects in C*-theory, we revisit an older result concerning the existence of the \v{S}ilov ideal. The direct proof of Hamana's theorem for the…
A compact quantum metric space is a unital $C^*$-algebra equipped with a Lip-norm. Let $\{(A_n, L_n)\}$ be a sequence of compact quantum metric spaces, and let $\phi_n:A_n\to A_{n+1}$ be a unital $^*$-homomorphism preserving Lipschitz…
In the final paper of the Graph Minors series N. Robertson and P. Seymour proved that graphs are well-quasi-ordered under the immersion ordering. A direct implication of this theorem is that each class of graphs that is closed under taking…
The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising…
We consider a family of norms (called operator E-norms) on the algebra $B(H)$ of all bounded operators on a separable Hilbert space $H$ induced by a positive densely defined operator $G$ on $H$. Each norm of this family produces the same…
It is shown that the class of Fredholm operators over an arbitrary unital $C^{*}$--algebra, which may not admit adjoint ones, can be extended in such a way that this class of compact operators, used in the definition of the class of…
We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we…
We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundamental techniques from the theory of order unit spaces and…
We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…
We develop a matricial version of Rieffel's Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C*-algebras. Our approach yields a metric space of ``isometric'' unital complete order…
We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next, we show that WEP is equivalent to a…
We prove a factorization of completely bounded maps from a $C^*$-algebra $A$ (or an exact operator space $E\subset A$) to $\ell_2$ equipped with the operator space structure of $(C,R)_\theta$ ($0<\theta<1$) obtained by complex interpolation…
We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…