Tauberian conditions for Conull spaces. (1985)

• Record Type: Journal Article
• Authors: Connor, J.; Snyder, A. K.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 8:Number 4(1985)
• Page Start: 689
• Page End: 692
• Publication Date: 1985
• Subjects: FK space; conull; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S016117128500076X
• Languages: English
• ISSNs: 0161-1712

Abstract

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.