Majorization and arithmetic mean ideals

TL;DR

This paper advances the theory of majorization for infinite sequences, linking it to operator ideals and convexity, and extends classical finite sequence results to the infinite case.

Contribution

It introduces new results on infinite majorization, connecting it to operator ideals and invariance properties, extending finite sequence majorization theory.

Findings

Extended finite majorization results to infinite sequences

Linked majorization properties to operator ideals and convexity

Characterized arithmetic mean closed operator ideals

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.