Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-17T16:16:13.660Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrix Transformations in an Incomplete Space

Published online by Cambridge University Press:  20 November 2018

I. J. Maddox
I. J. Maddox*
Affiliation:
University of Lancaster, Lancaster, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 727 - 734
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Hardy, G. H., Divergent series (Oxford Univ. Press, Oxford, 1949).Google Scholar
2. Kothe, G. and Teoplitz, O., Lineare Rdume mit unendlich vielen Koordinaten una Ringe unendlicher Matrizen, J. Reine Angew. Math., 171 (1934), 193–226.Google Scholar
3. Lorentz, G. G. and MacPhail, M. S., Unbounded operators and a theorem of A. Robinsonf Trans. Roy. Soc. Canada, Sect. Ill, 46 (1952), 33–37.Google Scholar
4. Ramanujan, M. S., Generalised Kojima-Toeplitz matrices in certain linear topological spaces, Math. Ann., 159 (1965), 365–373.Google Scholar
5. Robinson, A., On functional transformations and summability, Proc. London Math. Soc, 52 (1950), 132–160.Google Scholar
6. Toeplitz, O., Ûber allgemeine lineare Mittelbildungen, Prace Mat. Fiz., 22 (1911), 113–119.Google Scholar
7. Wilansky, A., An application of Banach linear functional to summability, Trans. Amer. Math. Soc, 67 (1949), 59–68.Google Scholar