2007/04/25 by Gelu Popescu, Popescu, Gelu
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.0704.3387
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.