Related papers: Omitting types in operator systems

Let $A$ be a unital $C^*$-algebra containing a closed two-sided ideal $J$ and an operator system $X$. We enlarge $X$ to an operator system $\mathcal{S}(X,J)$ in $\mathbb{M}_2(A)$, and show that in order for $\mathcal{S}(X,J)$ to be…

We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular, we can allow some infinite sum relations. We prove a…

In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…

Some recent research on the tensor products of operator systems and ensuing nuclearity properties in this setting raised many stability problems. In this paper we examine the preservation of these nuclearity properties including exactness,…

An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

We introduce an operator system, universal for the probabilistic models of a contextuality scenario, and identify its maximal C*-cover via the right C*-algebra of a canonical ternary ring of operators, arising from a hypergraph version of…

For $p\in [1,\infty)$, we show that every unital $L^p$-operator algebra contains a unique maximal $C^*$-subalgebra, which is always abelian if $p\neq 2$. Using this, we canonically associate to every unital $L^p$-operator algebra $A$ an…

We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of…

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…

We transfer the theory of slack operators and sums-of-squares-criteria for lifts from convex cones to operator systems. These allow to study the following question, among others: Given an abstract operator system, is its enveloping…

We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for the $L^p$-uniqueness of the Ornstein-Uhlenbeck operator and its integer powers defined on suitable algebras of functions…

Let $E$ be a Banach space that does not contain any copy of $\ell^1$ and $\A$ be a non commutative $C^*$-algebra. We prove that every absolutely summing operator from $\A$ into $E^*$ is compact, thus answering a question of Pe\l czynski. As…

We propose a generalization of K-theory to operator systems. Motivated by spectral truncations of noncommutative spaces described by $C^*$-algebras and inspired by the realization of the K-theory of a $C^*$-algebra as the Witt group of…

We study restriction and extension properties for states on C$^*$-algebras with an eye towards hyperrigidity of operator systems. We use these ideas to provide supporting evidence for Arveson's hyperrigidity conjecture. Prompted by various…

We observe that Kirchberg's QWEP conjecture is equivalent to the statement that $C^*(\mathbb{F})$ is elementarily equivalent to a QWEP C$^*$ algebra. We also make a few other model-theoretic remarks about WEP and LLP C$^*$ algebras.

We first generalize the logarithmic tensor category theory of Huang-Lepowsky-Zhang to the more general case that the module category for a vertex operator algebra $V$ (more generally a M\"{o}bius vertex algebra) might not be closed under…

We generalize Kirchberg's weak exactness to inclusions of C*-algebras in von Neumann algebras and study some characterizations and permanence properties which are similar to those of exact groups. We then consider a similar condition to…

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also…

In this paper, we show that the lattice of C*-covers of a non-selfadjoint operator algebra is either one point or uncountable. We prove that there are non-selfadjoint operator algebras with a one-point lattice in two ways: as an explicit…