On the nonequivalence of conservative Hausdorff methods and Hausdorff moment sequences
John Edwards, Stanley G. Wayment · Pacific Journal of Mathematics · 1971
In this paper we give a counter example to the theorem: A Hausdorff method is convergence preserving if and only if it is generated by a moment sequence as stated in "vectorvalued summability methods on a linear normed space" by L. C. Kurtz and D. H. Tucker, Proc.Amer.Math.Soc.16 (1965) 419-428.New results are also obtained which extend those known on the equivalence of the generalized Hausdorff moment problem with a generalized Riesz Representation Theorem, and a class of normed spaces is given in which the above mentioned does hold.The key tool in establishing these is the ^-integral.