Raphael Clouatre

collaborators

5 papers

math.OA2025

Rigidity of operator systems: tight extensions and noncommutative measurable structures

RaphaÃ«l ClouÃ¢tre, Ian Thompson

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 repr…

math.OA2025

Null projections and noncommutative function theory in operator algebras

David P. Blecher, RaphaÃ«l ClouÃ¢tre

We study projections in the bidual of a $C^{*}$ -algebra $B$ that are null with respect to a subalgebra $A$ , that is projections $p \in B^{**}$ satisfying $∣ I ¨ ∣ (p) = 0$ for every $Ï\in…

math.FA2025

Annihilating ideals and Agler--McCarthy spectral varieties in the bidisc

RaphaÃ«l ClouÃ¢tre, Poornendu Kumar

The closed unit bidisc $D^{2}$ is known to be a spectral set for any pair $(T_{1}, T_{2})$ of commuting contractions. When each $T_{i}$ is pure and has finite defect, th…

math.OA2025

$C^{*}$ -supports and abnormalities of operator systems

RaphaÃ«l ClouÃ¢tre, Colin Krisko

Let $S$ be a concrete operator system represented on some Hilbert space $H$ . A $C^{*}$ -support of $S$ is the $C^{*}$ -algebra generated (via the Choi--Effros product) by $S$ inside an i…

math.OA2024

Restrictions of pure states to subspaces of $C^{*}$ -algebras

RaphaÃ«l ClouÃ¢tre

Through the lens of noncommutative function theory, we study restrictions of pure states to unital subspaces of $C^{*}$ -algebras, in the spirit of the Kadison--Singer question. More…

Rigidity of operator systems: tight extensions and noncommutative measurable structures

Null projections and noncommutative function theory in operator algebras

Annihilating ideals and Agler--McCarthy spectral varieties in the bidisc

C∗-supports and abnormalities of operator systems

Restrictions of pure states to subspaces of C∗-algebras

$C^{*}$ -supports and abnormalities of operator systems

Restrictions of pure states to subspaces of $C^{*}$ -algebras