Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-20T11:44:36.192Z Has data issue: false hasContentIssue false
  • English
  • Français

Families of Sequences of 0s and 1s In FK-Spaces

Published online by Cambridge University Press:  20 November 2018

John Sember
John Sember*
Affiliation:
Simon Fraser University, Burnaby, B.C. V5A 1S6
Rights & Permissions [Opens in a new window]

Abstract

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.

A characterization is given of those families ℱ of subsets of the positive integers for which σ(ℓ1, ) is sequentially complete, where denotes the linear span of the characteristic functions of ℱ. Consequences include some known matrix results, such as Hahn's Theorem and conditions required for a matrix to "sum" the characteristic functions of the lacunary sets.

Keywords

46A4540A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 18 - 23
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Bennett, G., A new class of sequence spaces with applications in summability theory, Jour, reine angew. Math. 266 (1974), 49–75.Google Scholar
2. Bennett, G. and Kalton, N. J., Inclusion theorems for K-spaces, Can. J. Math. Vol. XXV, No. 3, 1973, 511–524.Google Scholar
3. Bennett, G. and Kalton, N. J., FK-spaces containing c0, Duke Math. J., 39(3), 1972, 561–582.Google Scholar
4. Brown, T. C. and Freedman, A. R., Arithmetic progressions in lacunary sets, Rocky Mountain J. of M., Vol. 17, No. 3, Summer 1987.Google Scholar
5. Edwards, R. E., Fourier series, Vol. 2, Springer Verlag, New York, 1967.Google Scholar
6. Lopez, J. M. and Ross, K. A., Sidon sets, Lecture notes in pure and applied mathematics, Vol. 13, Marcel Dekker, 1975.Google Scholar
7. Sember, J. J. and Freedman, A. R., On summing sequences ofO's and I's, Rocky Mountain J. of Math., Vol. 11, No. 3, Summer, 1981, 419–425.Google Scholar
8. Wilansky, A., Summability through functional analysis, North-Holland (Mathematics Studies No. 85) 1984.Google Scholar