Majorization and arithmetic mean ideals

2012/01/23 by Victor Kaftal, V. Kaftal, Kaftal, V. +3
Mathematics · #15A51 #47L20 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #math.FA #msc:15A51 #msc:47L20

paper · pdf · doi:10.48550/arxiv.1201.4826

To appear in Indiana University Mathematics Journal

arxiv created 2012/01/23 · openalex publication_date 2012/01/23 · arxiv updated 2012/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following "An infinite dimensional Schur-Horn theorem and majorization theory", Journal of Functional Analysis 259 (2010) 3115-3162, this paper further studies majorization for infinite sequences. It extends to the infinite case classical results on "intermediate sequences" for finite sequence majorization. These and other infinite majorization properties are then linked to notions of infinite convexity and invariance properties under various classes of substochastic matrices to characterize arithmetic mean closed operator ideals and arithmetic mean at infinity closed operator ideals.

Citations

• Traces on operator ideals and arithmetic means
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix

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