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FK spaces which include strongly summable sequences

Published online by Cambridge University Press:  24 October 2008

I. J. Maddox
I. J. Maddox
Affiliation:
Queen's University of Belfast
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Extract

The following interesting result on strongly summable sequences is due to Kuttner (2).

Theorem 1. Let 0 < p < 1. Then given any Toeplitz matrix A there is a sequence summable wp which is not summable A.

As usual, for 0 < p < ∞, we denote by wp the space of strongly summable sequences with index p. Thus x = (xk) ∈ wp if and only if there is a number l such that

Strongly summable sequences arise in the theory of Fourier series, see e.g. (8), Chapter X, in Ergodic theory, see e.g. (1), as well as in summability theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 131 - 134
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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