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Displaying similar documents to “Almost none of the sequences of 0's and 1's are almost convergent.”

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...

Some λ -sequence spaces defined by a modulus

Eberhard Malkowsky, Ekrem Savaş (2000)

Archivum Mathematicum

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The main object of this paper is to introduce and study some sequence spaces which arise from the notation of generalized de la Vallée–Poussin means and the concept of a modulus function.