On the nonequivalence of conservative Hausdorff methods and Hausdorff moment sequences

John R. Edwards and Stanley G. Wayment

Vol. 38 (1971), No. 1, 39–47

DOI: 10.2140/pjm.1971.38.39

Abstract

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 v-integral.

Mathematical Subject Classification 2000

Primary: 40D25

Secondary: 44A50

Milestones

Received: 3 June 1970

Published: 1 July 1971