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Norms of summation methods

Published online by Cambridge University Press:  24 October 2008

G. M. Petersen
G. M. Petersen
Affiliation:
University College of Swansea
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Extract

We shall understand the norm, h(A) of a regular matrix A = (amn) to be

The method has a norm, ‖ ‖, ‖ ‖ ≥ 1, given by ‖ ‖ = inf h(A) where the inf is taken over all the matrix methods equivalent to for bounded sequences (b-equivalent). These definitions are due essentially to Brudno(1) though his definition of

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 3 , July 1958 , pp. 354 - 357
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

(1)Brudno, A.Summation of bounded sequences by matrices. Rec. Math. (Mat. Sbornik) N.S., 16 (1945), 191–247 (in Russian).Google Scholar
(2)Lorentz, G. G.A contribution to the theory of divergent sequences. Acta Math., Stockh., 80 (1948), 167–90.CrossRefGoogle Scholar
(3)Petersen, G. M. Matrix norms. (Unpublished.)Google Scholar
(4)Petersen, G. M.Summability methods and bounded sequences. J. Lond. Math. Soc. 31 (1956), 324–6.CrossRefGoogle Scholar
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