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A note on a theorem of Maddox on strong almost convergence

Published online by Cambridge University Press:  24 October 2008

G. Das  and
S. K. Mishra
G. Das
Affiliation:
Utkal University, Bhubaneswar, India
S. K. Mishra
Affiliation:
Utkal University, Bhubaneswar, India
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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

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References

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