Tauberian conditions for Conull spaces. (1985) - Connor, J.; Snyder, A. K.
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.