2017/03/01 by Wafaa Albar, Wafaa A. Albar, Albar, Wafaa +4 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Arithmetic #Computer science #Constant (computer programming) #Degree (music) #Dimension (graph theory) #Discrete mathematics #FOS: Mathematics #Geometric mean #Inequality #Inequality of arithmetic and geometric means #Log sum inequality #Mathematical Inequalities and Applications #Mathematical analysis #Mathematics #Noncommutative geometry #Operator Algebras (math.OA) #Order (exchange) #Pure mathematics #Random Matrices and Applications #Rearrangement inequality #Statistics #math.OA
paper · pdf · doi:10.48550/arxiv.1703.00546
published in arXiv (Cornell University) (Cornell University) · 28 pages
arxiv created 2017/03/01 · openalex publication_date 2017/03/01 · arxiv updated 2017/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recht and Ré introduced the noncommutative arithmetic geometric mean inequality (NC-AGM) for matrices with a constant depending on the degree d and the dimension m. In this paper we prove AGM inequalities with a dimension-free constant for general operators. We also prove an order version of the AGM inequality under additional hypothesis. Moreover, we show that our AGM inequality almost holds for many examples of random matrices .