A note on a theorem of Maddox on strong almost convergence
Published online by Cambridge University Press: 24 October 2008
Extract
Let m be the set of all real sequences x = (xn) with norm . A linear functional L on m is said to be a Banach limit (see Banach(1), p. 32) if it has the following properties:
(i) L(x) ≥ 0, if x ≥ 0 (i.e. xn ≥ 0, for all n ∈ N)
(ii) L{e) = 1, where e = (1, 1, 1,…),
(iii) L(Sx) = L(x), where (Sx)n = xn+1.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 3 , May 1981 , pp. 393 - 396
- Copyright
- Copyright © Cambridge Philosophical Society 1981
References
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