6 papers · 1 filter
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…
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…
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…