On some generalizations of Lorentz's almost convergence |
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Authors: | S Mercourakis G Vassiliadis |
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Institution: | aUniversity of Athens, Department of Mathematics, 15784 Athens, Greece |
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Abstract: | We investigate an extension of the almost convergence of G.G. Lorentz, further weakening the notion of M-almost convergence we defined in S. Mercourakis, G. Vassiliadis, An extension of Lorentz's almost convergence and applications in Banach spaces, Serdica Math. J. 32 (2006) 71–98] and requiring that the means of a bounded sequence restricted on a subset M of converge weakly in ℓ∞(M). The case when M has density 1 is of special interest and in this case we derive a result in the direction of the Mean Ergodic Theorem (see Theorem 2). |
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Keywords: | Almost convergence Shift operator Banach limit Weak convergence |
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