2014/12/26 by Katrien Audenaert, K. M. R. Audenaert, Audenaert, K. M. R. +3 · 1 citation
Mathematics · #15A16 #15A42 #47A64 #Advanced Operator Algebra Research #Combinatorics #FOS: Mathematics #Functional Analysis (math.FA) #Lie group #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Positive-definite matrix #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.FA #msc:15A16 #msc:15A42 #msc:47A64
paper · pdf · doi:10.48550/arxiv.1412.7905
26 pages
arxiv created 2014/12/26 · openalex publication_date 2014/12/26 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A and B be positive semidefinite matrices. The limit of the expression Zp:=(Ap/2BpAp/2)1/p as p tends to 0 is given by the well known Lie-Trotter-Kato formula. A similar formula holds for the limit of Gp:=(Ap # Bp)2/p as p tends to 0, where X # Y is the geometric mean of X and Y. In this paper we study the complementary limit of Zp and Gp as p tends to ∞, with the ultimate goal of finding an explicit formula, which we call the anti Lie-Trotter formula. We show that the limit of Zp exists and find an explicit formula in a special case. The limit of Gp is shown for 2×2 matrices only.