Almost convergence and triple band matrix
The concept of almost convergence of a bounded sequence x = (x(k)) was introduced by means of Banach Limits by G.G. Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948) 167-190]. The space of almost convergent sequences is denoted by f. In this paper, we introduce f (B), which is the domain of triple band matrix B(r, s, t) in the sequence space f, determine the beta- and gamma-duals of the spaces f (B) and characterize the classes (f (B) : Y) and (Y : f (B)), where Y is any given sequence space. Finally, we also give the characterizations of some other classes as an application of those main results. Published by Elsevier Ltd
almost convergence beta- and gamma-duals matrix domain of a sequence space schauder basis matrix transformations