English

Noncommutative Berezin transforms and model theory

Functional Analysis 2007-05-23 v1 Operator Algebras

Abstract

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.

Keywords

Cite

@article{arxiv.0704.3387,
  title  = {Noncommutative Berezin transforms and model theory},
  author = {Gelu Popescu},
  journal= {arXiv preprint arXiv:0704.3387},
  year   = {2007}
}
R2 v1 2026-06-21T08:22:17.942Z