2019/12/21 by Raphaël Clouâtre, Clouâtre, Raphaël, Edward J. Timko +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1912.10331
openalex publication_date 2019/12/21 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28
The main objects under study are quotients of multiplier algebras of certain\ncomplete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson\nspace on the ball and the Dirichlet space on the disc. We are particularly\ninterested in the non-commutative Choquet boundaries for these quotients.\nArveson's notion of hyperrigidity is shown to be detectable through the\nessential normality of some natural multiplication operators, thus extending\npreviously known results on the Arveson--Douglas conjecture. We also highlight\nhow the non-commutative Choquet boundaries of these quotients are intertwined\nwith their Gelfand transforms being completely isometric. Finally, we isolate\nanalytic and topological conditions on the so-called supports of the underlying\nideals that clarify the nature of the non-commutative Choquet boundaries.\n