Stephen Montgomery-Smith and Evgueni Semenov, Rearrangements and Operators. 25 Years of Voronezh Winter Mathematical School, Proceedings in honor of S. Krein, A.M.S. Let \(m = (m_{i,j})\) be an \(n\) by \(n\) matrix. Pick a permutation \(\pi\) of \(\{1,2,\dots,n\}\) at random. Kwapien and Schütt considered the problem of finding \(E\left(\left\|(m_{i,\pi(i)})\right\|_p^q\right)^{1/q}\). In this paper, we generalize their results to rearrangement invariant spaces. We also consider the property of \(D\) and \(D^*\) convexity for rearrangement invariant spaces. (tex, dvi, ps, pdf. The tex file also requires ams-p.sty, ams-spec.sty, amsppt.sti, amsppt.sty and gen-p.sty).


 List of all preprints