Let $ S $ be an operator system–a self-adjoint linear subspace of a unital $ C^* $-algebra $
A $ such that $\mathbf 1\in S $ and $ A= C^*(S) $ is generated by $ S $. A boundary …

In this paper we extend the traditional framework of noncommutative geometry in order to
deal with spectral truncations of geometric spaces (ie imposing an ultraviolet cutoff in …

We show that every operator system (and hence every unital operator algebra) has
sufficiently many boundary representations to generate the C*-envelope. We solve a 45 …

Given linear matrix inequalities (LMIs) L 1 and L 2 it is natural to ask:(Q 1) when does one
dominate the other, that is, does L_1 (X) ⪰ 0 imply L_2 (X) ⪰ 0?(Q 2) when are they mutually …

We introduce a new and extensive theory of noncommutative convexity along with a
corresponding theory of noncommutative functions. We establish noncommutative …

We study reproducing kernel Hilbert spaces on the unit ball with the complete Nevanlinna–
Pick property through the representation theory of their algebras of multipliers. We give a …

A (finite or countably infinite) set G of generators of an abstract C*-algebra A is called
hyperrigid if for every faithful representation of A on a Hilbert space A⊆ B (H) and every …

A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction
by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly …

We examine the semicrossed products of a semigroup action by∗-endomorphisms on a C*-
algebra, or more generally of an action on an arbitrary operator algebra by completely …

Dilation theory is a paradigm for studying operators by way of exhibiting an operator as a
compression of another operator which is in some sense well behaved. For example, every …