International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 689-692
doi:10.1155/S016117128500076X
Tauberian conditions for Conull spaces
1Department of Mathematical Sciences, Kent State University, Kent 44242, Ohio, USA
2Department of Mathematics, Lehigh University, Bethlehem 18015, PA, USA
Received 15 February 1984
Copyright © 1985 J. Connor and A. K. Snyder. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The typical Tauberian theorem asserts that a particular summability method
cannot map any divergent member of a given set of sequences into a convergent sequence. These sets of sequences are typically defined by an “order growth” or “gap” condition. We establish that any conull space contains a bounded divergent member of such a set;
hence, such sets fail to generate Tauberian theorems for conull spaces.