Domain of the Nörlund Matrix in Some of Maddox’s Spaces

Maddox defined the sequence spaces ??(p) , c(p) and c0(p) in Maddox (Q J Math Oxf Lond 18(2):345–355, 1967) and Maddox (Proc Comb Phil Soc 64:335–340, 1968), respectively. In the present paper, following Yeşilkayagil and Başar (Abstr Appl Anal, 2014), the Nörlund sequence spaces ??(Nt, p) , c(Nt, p) and c0(Nt, p) of non-absolute type are introduced and it is proved that those sequence spaces are linearly isomorphic to the spaces ??(p) , c(p) and c0(p) , respectively. The ?-, ?- and ?-duals of the spaces ??(Nt, p) , c(Nt, p) and c0(Nt, p) are determined and the bases of the spaces c(Nt, p) and c0(Nt, p) are given. Besides this, the classes of matrix transformations from ??(Nt, p) to ??, f, f0, c, c0 and from ?(p) to ?(Nt, p) are characterized, where ?, ? denote any of the classical sequence spaces ??, c or c0. © 2017, The National Academy of Sciences, India