Related papers: A Finite Dimensional Counterexample for Arveson's …
Let $A$ be a unital $C^*$-algebra generated by some separable operator system $S$. More than a decade ago, Arveson conjectured that $S$ is hyperrigid in $A$ if all irreducible representations of $A$ are boundary representations for $S$.…
Arveson's hyperrigidity conjecture predicts that if the non-commutative Choquet boundary of a separable operator system $\mathcal{S}$ is the entire spectrum of its generated C*-algebra $\mathcal{B}$ then $\mathcal{S}$ is hyperrigid in…
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…
In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given…
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…
We prove that for every compact, convex subset $K\subset\mathbb{R}^2$ the operator system $A(K)$, consisting of all continuous affine functions on $K$, is hyperrigid in the C*-algebra $C(\mathrm{ex}(K))$. In particular, this result implies…
We explore connections between boundary representations of operator spaces and those of the associated Paulsen systems. Using the notions of finite representation and separating property which we introduced, boundary representations for…
In this paper we give a decomposition of a state on a $C^*$-algebra into a family of pure states and a decomposition of a representation into a family of irreducible representation. Then, we use it to solve the following three problems…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
We prove that every bounded self-adjoint operator in Hilbert space is a real linear combination of $4$ orthoprojections. Also we show that operators of the form identity minus compact positive operator can not be decomposed in a real linear…
The rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} are established and all the irreducible modules are constructed and classified. This is part of classification of rational vertex operator…
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 show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff's operator also has this property on the space of…
Given a countable dense subset D of an infinite-dimensional separable Hilbert space H the set of operators for which every vector in D except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology…
In our paper "Essential normality, essential norms and hyperrigidity" we claimed that the restriction of the identity representation of a certain operator system (constructed from a polynomial ideal) has the unique extension property,…
A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra $\hat{H}_{4}$ with some natural conditions. It turns out the representation theory of $\hat{H}_{4}$ is quite different from the theory of representations…
Arveson's extension theorem asserts that B(H) is an injective object in the category of operator systems. Calling every self adjoint unital subspace of a unital *-algebra, a quasi operator system, we show that Arveson's theorem remains…