Matrix limit theorems of Kato type related to positive linear maps and operator means

2018/10/12 by Fumio Hiai, Hiai, Fumio
Mathematics · #15A42 #15A45 #47A64 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #math.FA #msc:15A42 #msc:15A45 #msc:47A64

paper · pdf · doi:10.48550/arxiv.1810.05476

23 pages

arxiv created 2018/10/12 · openalex publication_date 2018/10/12 · arxiv updated 2018/10/15 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

We obtain limit theorems for Φ(A^p)^1/p and (A^pσB)^1/p as p→∞ for positive matrices A,B, where Φ is a positive linear map between matrix algebras (in particular, Φ(A)=KAK^*) and σ is an operator mean (in particular, the weighted geometric mean), which are considered as certain reciprocal Lie-Trotter formulas and also a generalization of Kato's limit to the supremum A\vee B with respect to the spectral order.

Related

• Anti Lie-Trotter formula
• Inequalities and limits of weighted spectral geometric mean
• Matrix power means and new characterizations of operator monotone functions
• Extensions of Yamamoto-Nayak's Theorem
• On matrix inequalities between the power means: counterexamples