English

On conjugate systems with respect to completely positive maps

Operator Algebras 2025-11-03 v2

Abstract

We study the operator-valued partial derivative associated with covariance matrices on a von Neumann algebra B. We provide a cumulant characterization for the existence of conjugate variables and study some structure implications of their existence. Namely, we show that the center of the von Neumann algebra generated by B and its relative commutant is the center of B.

Keywords

Cite

@article{arxiv.2412.14336,
  title  = {On conjugate systems with respect to completely positive maps},
  author = {Yoonkyeong Lee},
  journal= {arXiv preprint arXiv:2412.14336},
  year   = {2025}
}
R2 v1 2026-06-28T20:41:18.257Z