10 citations · 24 across the 19 of their papers we have counts for
30 papers
Annihilating ideals and Agler--McCarthy spectral varieties in the bidisc
Raphaël Clouâtre, Poornendu Kumar
The closed unit bidisc is known to be a spectral set for any pair of commuting contractions. When each is pure and has finite defect, th…
-supports and abnormalities of operator systems
Raphaël Clouâtre, Colin Krisko
Let be a concrete operator system represented on some Hilbert space . A -support of is the -algebra generated (via the Choi--Effros product) by inside an i…
Rigidity of operator systems: tight extensions and noncommutative measurable structures
Raphaël Clouâtre, Ian Thompson
Let be a unital -algebra generated by some separable operator system . More than a decade ago, Arveson conjectured that is hyperrigid in if all irreducible repr…
Null projections and noncommutative function theory in operator algebras
David P. Blecher, Raphaël Clouâtre
We study projections in the bidual of a -algebra that are null with respect to a subalgebra , that is projections satisfying for every $ϕ\in B^…
A boundary projection for the dilation order
Raphaël Clouâtre, Hridoyananda Saikia
Motivated by Arveson's conjecture, we introduce a notion of hyperrigidity for a partial order on the state space of a -algebra . We show how this property is equivalent to…
Restrictions of pure states to subspaces of -algebras
Raphaël Clouâtre
Through the lens of noncommutative function theory, we study restrictions of pure states to unital subspaces of -algebras, in the spirit of the Kadison--Singer question. More…
Lebesgue decompositions and the Gleason--Whitney property for operator algebras
Raphaël Clouâtre, Michael Hartz
Broadly speaking, this paper is concerned with dual spaces of operator algebras. More precisely, we investigate the existence of what we call Lebesgue projections: central projecti…
Minimal boundaries for operator algebras
Raphaël Clouâtre, Ian Thompson
We study boundaries for unital operator algebras. These are sets of irreducible -representations that completely capture the spatial norm attainment for a given subalgebra. Clas…
Non-commutative measure theory: Henkin and analytic functionals on -algebras
Raphaël Clouâtre, Edward J. Timko
Henkin functionals on non-commutative -algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our…
Analytic functionals for the non-commutative disc algebra
Raphaël Clouâtre, Robert T. W. Martin, Edward J. Timko
The main objects of study in this paper are those functionals that are analytic in the sense that they annihilate the non-commutative disc algebra. In the classical univariate case…
Finite-dimensional approximations and semigroup coactions for operator algebras
Raphaël Clouâtre, Adam Dor-On
The residual finite-dimensionality of a -algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional rep…
Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and -liminality
Raphaël Clouâtre, Ian Thompson
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 rep…
Gelfand transforms and boundary representations of complete Nevanlinna--Pick quotients
Raphaël Clouâtre, Edward J. Timko
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 th…
Localizable points in the support of a multiplier ideal and spectra of constrained operators
Raphaël Clouâtre, Edward J. Timko
A unitarily invariant, complete Nevanlinna--Pick kernel on the unit ball determines a class of operators on Hilbert space called -contractions. We study those -contractio…
Multipliers and operator space structure of weak product spaces
Raphaël Clouâtre, Michael Hartz
In the theory of reproducing kernel Hilbert spaces, weak product spaces generalize the notion of the Hardy space . For complete Nevanlinna-Pick spaces , we charact…
A Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factor
Raphaël Clouâtre, Michael Hartz, Dominik Schillo
We provide a short argument to establish a Beurling-Lax-Halmos theorem for reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick factor. We also record fact…
Row contractions annihilated by interpolating vanishing ideals
Raphaël Clouâtre, Edward J. Timko
We study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-ty…
Cyclic row contractions and rigidity of invariant subspaces
Raphaël Clouâtre, Edward J. Timko
It is known that pure row contractions with one-dimensional defect spaces can be classified up to unitary equivalence by compressions of the standard -shift acting on the full F…
Joint similarity for commuting families of power bounded matrices
Raphaël Clouâtre, Diarra Mbacke
An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each opera…
Residually finite-dimensional operator algebras
Raphaël Clouâtre, Christopher Ramsey
We study non-selfadjoint operator algebras that can be entirely understood via their finite-dimensional representations. In contrast with the elementary matricial description of fi…
Non-commutative peaking phenomena and a local version of the hyperrigidity conjecture
Raphaël Clouâtre
We investigate various notions of peaking behaviour for states on a -algebra, where the peaking occurs within an operator system. We pay particularly close attention…
Unperforated pairs of operator spaces and hyperrigidity of operator systems
Raphaël Clouâtre
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…
Completely bounded isomorphisms of operator algebras and similarity to complete isometries
Raphaël Clouâtre
A well-known theorem of Paulsen says that if is a unital operator algebra and is a unital completely bounded homomorphism, then …
Spectral and homological properties of Hilbert modules over the disc algebra
Raphaël Clouâtre
We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds…