# Non‐commutative peaking phenomena and a local version of the hyperrigidity conjecture

@article{Clouatre2017NoncommutativePP, title={Non‐commutative peaking phenomena and a local version of the hyperrigidity conjecture}, author={Raphael Clouatre}, journal={Proceedings of the London Mathematical Society}, year={2017}, volume={117} }

We investigate various notions of peaking behaviour for states on a C∗ ‐algebra, where the peaking occurs within an operator system. We pay particularly close attention to the existence of sequences of elements forming an approximation of the characteristic function of a point in the state space. We exploit such characteristic sequences to localise the C∗ ‐algebra at a given state, and use this localisation procedure to verify a variation of Arveson's hyperrigidity conjecture for arbitrary…

## 6 Citations

Strongly Peaking Representations and Compressions of Operator Systems

- MathematicsInternational Mathematics Research Notices
- 2020

We use Arveson’s notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets that admit minimal presentations. A fully compressed…

Gelfand transforms and boundary representations of complete Nevanlinna–Pick quotients

- MathematicsTransactions of the American Mathematical Society
- 2020

The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball and the Dirichlet space…

Finite Dimensionality in the Non-commutative Choquet Boundary: Peaking Phenomena and C*-Liminality

- MathematicsInternational Mathematics Research Notices
- 2021

We explore the finite-dimensional part of the non-commutative Choquet boundary of an operator algebra. In other words, we seek finite-dimensional boundary representations. Such representations may…

Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and $\mathrm{C}^*$-liminality.

- Mathematics
- 2020

We explore the finite-dimensional part of the non-commutative Choquet boundary of an operator algebra. In other words, we seek finite-dimensional boundary representations. Such representations may…

Boundary representations and rectangular hyperrigidity

- Mathematics
- 2020

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…

On Vector-Valued Characters for Noncommutative Function Algebras

- MathematicsComplex Analysis and Operator Theory
- 2020

Let A be a closed subalgebra of a $$C^*$$ C ∗ -algebra, that is a norm-closed algebra of Hilbert space operators. We generalize to such operator algebras several key theorems and concepts from the…

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