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}
}