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The norm of iterations of regular matrices

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

By an iteration of a regular summation matrix B = (bmn) with a regular matrix A = (amn), or B.A, we shall mean the summation method defined by the matrix B operating on the sequence {tn} of A transforms of a sequence {sn}. Thus the sequence {τn} of B. A is given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 286 - 289
Copyright
Copyright © Cambridge Philosophical Society 1957

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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)Goffman, C. and Petersen, G. M.Submethods of regular matrix summability methods. Canad. J. Math. 8 (1956), 40–6.Google Scholar
(3)Petersen, G. M.Summability methods and bounded sequences. J. Lond. Math. Soc. 31 (1956), 324–6.CrossRefGoogle Scholar