Abstract

The concept of almost convergence of a bounded sequence x=(xk) 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 β- 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.

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