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Summability and bounded sequences

Published online by Cambridge University Press:  24 October 2008

G. M. Petersen
G. M. Petersen
Affiliation:
University of New Mexico
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Extract

It is our purpose in this paper to present concise proofs of four theorems which take up the greater part of a paper due to Brudno (1). The proofs of Theorems 1 and 2 have appeared already ((2), (3)), but we present them again so that comparisons can be made with the other two.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 3 , July 1959 , pp. 257 - 261
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

(1)Brudno, A.Summation of bounded sequences by matrices. Mat. Sbornik, 16 (1945), 191–247 (in Russian).Google Scholar
(2)Petersen, G. M.Summability methods and bounded sequences. J. Lond. Math. Soc. 31 (1956), 324–6.CrossRefGoogle Scholar
(3)Petersen, G. M.Inclusion between limitation methods. Math. Z. 65 (1956), 494–6.CrossRefGoogle Scholar
(4)Petersen, G. M.The norm of iterations of regular matrices. Proc. Camb. Phil. Soc. 53 (1957), 286–9.CrossRefGoogle Scholar