Displaying similar documents to “Summation of almost convergent divergent Sequences, topological methods.”

An extension of Lorentz's almost convergence and applications in Banach spaces

Mercourakis, S., Vassiliadis, G. (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 40C99, 46B99. We investigate an extension of the almost convergence of G. G. Lorentz requiring that the means of a bounded sequence converge uniformly on a subset M of N. We also present examples of sequences α∈ l∞(N) whose sequences of translates (Tn α)n≥ 0 (where T is the left-shift operator on l∞(N)) satisfy: (a) Tn α, n ≥ 0 generates a subspace E(α) of l∞(N) that is isomorphically embedded into c0 while α is not almost...