2012/10/10 by Paul S. Muhly, Muhly, Paul S., Baruch Solel +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #math.CV #math.FA #math.OA #math.RA
paper · pdf · doi:10.48550/arxiv.1210.2964
arxiv created 2012/10/10 · openalex publication_date 2012/10/10 · arxiv updated 2012/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H∞(E) be the Hardy algebra of a W*-correspondence E over a W*-algebra M. Then the ultraweakly continuous completely contractive representations of H∞(E) are parametrized by certain sets AC(σ) indexed by NRep(M) - the normal *-representations σ of M. Each set AC(σ) has analytic structure, and each element F∈ H∞(E) gives rise to an analytic operator-valued function Fσ on AC(σ) that we call the σ-Berezin transform of F. The sets AC(σ)σ∈Σ and the family of functions Fσσ∈Σ exhibit "matricial structure" that was introduced by Joeseph Taylor in his work on noncommutative spectral theory in the early 1970s. Such structure has been exploited more recently in other areas of free analysis and in the theory of linear matrix inequalities. Our objective here is to determine the extent to which the matricial structure characterizes the Berezin transforms.