Some generalizations of the space bvpbvp of pp-bounded variation sequences

The spaces bvpbvp and bv∞bv∞ of sequences of pp-bounded variation have recently been introduced by Başar and Altay [F. Başar, B. Altay, On the space of sequences of pp-bounded variation and related matrix mappings, Ukrainian Math. J. 55 (1) (2003) 136–147], where 1≤p<∞1≤p<∞. In the present paper, the sequence spaces bv(u,p)bv(u,p) and bv∞(u,p)bv∞(u,p) of non-absolute type have been defined and it has been proved that the spaces bv(u,p)bv(u,p) and bv∞(u,p)bv∞(u,p) are linearly isomorphic to the spaces ℓ(p)ℓ(p) and ℓ∞(p)ℓ∞(p) of Maddox, respectively. Besides this, the αα-, ββ- and γγ-duals of the spaces bv(u,p)bv(u,p) and bv∞(u,p)bv∞(u,p) have been computed and the basis of the space bv(u,p)bv(u,p) has been constructed. The classes (bv(u,p):ℓ∞)(bv(u,p):ℓ∞) and (bv(u,p):c)(bv(u,p):c) of infinite matrices have been characterized and the characterizations of some other classes have also been derived by means of a given basic lemma. The final section of the paper has been devoted to some consequences about the rotundity of the space bv(u,p)bv(u,p).