2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127929We 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.41 pagesFunctional AnalysisOperator Algebras47A20; 47A56; 47A13; 47A63text