Moment sequences in Hilbert space
Gordon Johnson · Pacific Journal of Mathematics · 1973
Suppose / is a real valued function of bounded variation on [0,1].Then for each nonnegative integer n, the Stieltjes integral 1 j n df exists, where for each number x, j(x) = x.A Jo necessary and sufficient condition is given for / in order that the moment sequence for /, {C n }n=o, is square summable.A second result establishes that the set of all such square summable moment sequences is dense in I 2 .LEMMA 1.If p is a number, 1/2 < p < 1, and for each nonnegatίve integer n, a n = 1 -(n + l)~p then