Matrix transformations between the spaces of Cesàro sequences and invariant means

@article{Mursaleen2006MatrixTB,
  title={Matrix transformations between the spaces of Ces{\`a}ro sequences and invariant means},
  author={Mohammad Mursaleen and Ekrem Savas and M. Aiyub and Syed Abdul Mohiuddine},
  journal={Int. J. Math. Mathematical Sciences},
  year={2006},
  volume={2006},
  pages={74319:1-74319:8}
}
Let ω be the space of all sequences, real or complex, and let l∞ and c, respectively, be the Banach spaces of bounded and convergent sequences x = (xn) with norm ‖x‖ = supk≥0 |xk|. Let σ be a mapping of the set of positive integers into itself. A continuous linear functional φ on l∞ is said to be an invariant mean or a σmean if and only if (i) φ(x) ≥ 0, when the sequence x = (xn) has xn ≥ 0 for each n; (ii) φ(e) = 1, where e = (1,1,1, . . .); and (iii) φ((xσ(n)))= φ(x), x ∈ l∞. For certain… CONTINUE READING