  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.
