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The Unrestricted Section Properties of Sequences

Published online by Cambridge University Press:  20 November 2018

John Sember  and
Marc Raphael
John Sember
Affiliation:
Simon Fraser University, Burnaby, British Columbia
Marc Raphael
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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1. Introduction. An unrestricted section of a sequence x is any sequence of the form Σk∈Fxkδk, where F is some finite subset of the natural numbers. The notion of boundedness of the set of unrestricted sections of a sequence in a K-space was studied in [10], and called unconditional section boundedness (UAB). It was shown in [10] (Theorem 7) that the class of FK-spaces in which every element has UAB consists of those FK-spaces that are invariant under coordinatewise multiplication by the convergent sequences.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 331 - 336
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Buntinas, M., Convergent and bounded Cesàro sections in FK-spaces, Math. Z. 121 (1971), 191–200.Google Scholar
2. Buntinas, M., On Toeplitz sections in sequence spaces, Proc. Cambridge Philos. Soc. 78 (1975), 451–460.Google Scholar
3. Day, M. M., Normed linear spaces.(Berlin-Gôttingen-Heidelberg, 1962).Google Scholar
4. Garling, D. J. H., On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 997–1019.Google Scholar
5. Goes, G., Summen von FK-raumen, funktionale abschnittskonvergenz una Umkehrsatze, Tôhoku Math. J. 26 (1974), 487–504.Google Scholar
6. Goffman, C. and Pedrick, G., First course in functional analysis (Englewood Cliffs, N.J., 1965).Google Scholar
7. McArthur, C. W., On a theorem of Orlicz and Pettis, Pacific J. Math. 22 (1967), 297–302.Google Scholar
8. Robertson, A. P., On unconditional convergence in topological vector spaces, Proc. Roy. Soc. Edin., Sect. A 68 (II) (1969), 145–157.Google Scholar
9. Robertson, A. P. and Robertson, W. J., Topological vector spaces (Cambridge, 1964).Google Scholar
10. Sember, J. J., On unconditional section boundedness in sequence spaces, Rocky Mountain J. of Math. Vol. 7, No. 4, (1977).Google Scholar
11. Snyder, A. K., Conull and coregular FK-spaces, Math Z. 90, (1965), 376–381.Google Scholar
12. Wilansky, A., Functional analysis (New York, 1964).Google Scholar