Almost convergence and triple band matrix

The concept of almost convergence of a bounded sequence x=(xk)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 ff. In this paper, we introduce f(B)f(B), which is the domain of triple band matrix B(r,s,t)B(r,s,t) in the sequence space ff, determine the ββ- and gamma-duals of the spaces f(B)f(B) and characterize the classes (f(B):Y)(f(B):Y) and (Y:f(B))(Y:f(B)), where YY is any given sequence space. Finally, we also give the characterizations of some other classes as an application of those main results.