Majorization and arithmetic mean ideals Victor KaftalG. Weiss 15A5147L20majorization of sequencesoperator idealsarithmetic mean Following \emph{An infinite dimensional Schur-Horn theorem and majorization theory} [V. Kaftal and G. Weiss, \textit{An infinite dimensional Schur-Horn theorem and majorization theory}, J. Funct. Anal. \textbf{259} (2010), no.12, 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. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4603 10.1512/iumj.2011.60.4603 en Indiana Univ. Math. J. 60 (2011) 1393 - 1424 state-of-the-art mathematics http://iumj.org/access/