Relative modular operator in semifinite von Neumann algebras and its use

2019/12/20 by Andrzej Łuczak, Łuczak, Andrzej, Hanna Podsȩdkowska +3
Mathematics · #46L53 #81R15 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1912.09633

openalex publication_date 2019/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Rényi's relative entropy known in finite dimension.

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