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Matrix transformations between some classes of sequences

Published online by Cambridge University Press:  24 October 2008

C. G. Lascarides  and
I. J. Maddox
C. G. Lascarides
Affiliation:
University of Lancaster
I. J. Maddox
Affiliation:
University of Lancaster
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Extract

Let A = (ank) be an infinite matrix of complex numbers ank (n, k = 1, 2,…) and X, Y two subsets of the space s of complex sequences. We say that the matrix A defines a (matrix) transformation from X into Y, and we denote it by writing A: X → Y, if for every sequence x = (xk)∈X the sequence Ax = (An(x)) is in Y, where An(x) = Σankxk and the sum without limits is always taken from k = 1 to k = ∞. The sequence Ax is called the transformation of x by the matrix A. By (X, Y) we denote the class of matrices A such that A: X → Y.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 99 - 104
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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