Relative modular operator in semifinite von Neumann algebras and its use
Operator Algebras
2021-03-19 v2 Mathematical Physics
Functional Analysis
math.MP
Quantum Algebra
Quantum Physics
Abstract
We present some results concerning the relative modular operator in semifinite von Neumann algebras. These results allow one to prove some basic formula for trace, to obtain equivalence between Araki's relative entropy and Umegaki's information as well as to derive some formulae for quasi-entropies, and R\'enyi's relative entropy known in finite dimension.
Keywords
Cite
@article{arxiv.1912.09633,
title = {Relative modular operator in semifinite von Neumann algebras and its use},
author = {Andrzej Łuczak and Hanna Podsędkowska and Rafał Wieczorek},
journal= {arXiv preprint arXiv:1912.09633},
year = {2021}
}