2007/04/25 by Gelu Popescu, Popescu, Gelu
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Mathematics #Noncommutative geometry #Pure mathematics #math.FA #math.OA #msc:47A13 #msc:47A20 #msc:47A56 #msc:47A63
paper · pdf · doi:10.48550/arxiv.0704.3387
published in arXiv (Cornell University) (Cornell University) · 41 pages
arxiv created 2007/04/25 · openalex publication_date 2007/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space, which is generated by certain positivity conditions on polynomials in n noncommutative indeterminates. We obtain Fatou type results, functional calculi, and a model theory for n-tuples of operators in these domains. The main role in this study is played by a class of noncommutative Berezin transforms which is introduced in this paper. Our results extend to noncommutative varieties.