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Inclusion sets of regular summability matrices. III

Published online by Cambridge University Press:  24 October 2008

J. W. Baker  and
G. M. Petersen
J. W. Baker
Affiliation:
University College, Swansea, and University of Canterbury, Christchurch
G. M. Petersen
Affiliation:
University College, Swansea, and University of Canterbury, Christchurch
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Extract

Let A = (am, n) be a (regular summability) matrix. Then will denote the set of bounded sequences which are summed by A. If {Ai} (i = 1, 2, …, N) is a finite set of such matrices, and if consists of every bounded sequence then we shall say that the matrices span the bounded sequences. Ifx = {xn} belongs to then we denote the value to which A sums x by A-lim x. If y = {yn} is any sequence, then the A-transform of y (if it exists) is the sequence {Aμ(y)}, where

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 3 , July 1966 , pp. 389 - 394
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Baker, J. W. and Petersen, G. M.Inclusion of sets of regular summability matrices. Proc. Cambridge Philos. Soc. 60 (1964), 705–712.CrossRefGoogle Scholar
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