Abstract

The Abel-type matrix Aα,t was introduced and studied as a mapping into ℓ by Lemma (1999). The purpose of this paper is to study these transformations as mappings into Gw. The necessary and sufficient conditions for Aα,t to be Gw-Gw are established. The strength of Aα,t in the Gw-Gw setting is investigated. Also, it is shown that Aα,t is translative in the Gw-Gw senses for certain sequences.