Characterization of summability methods with high indices

Abstract

In this paper we establish a set of necessary and sufficient conditions in order that {pipe}C, 0{pipe}k› {pipe}R, pn{pipe}sand {pipe}R, pn{pipe}k? {pipe}C, 0{pipe}sfor the case 1 < k ? s < ?. As a corollary, we obtain that a crucial assumption of [BOR, H.: A new result on the high indices theorem, Analysis 29 (2009), 403-405] is omitted and that the other one is not only sufficient but also necessary for his consequence to hold. © 2013 Versita Warsaw and Springer-Verlag Wien.