10 papers
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-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…
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…