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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.

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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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