Characterization of ω -almost convergent sequences in Lp(T2)

Abstract

In this paper, we introduce the concept of ω -almost convergent sequences. Such a definition is a weak form of almost convergent sequences given by G. G. Lorentz in [Acta Math., Vol. 80 (1948), pp. 167–190]. We give Cauchy criterions for w -almost convergence and characterize ω -almost convergent double sequences in Lp(T2) in terms of Fourier coefficients.