Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T01:45:57.443Z Has data issue: false hasContentIssue false
  • English
  • Français

FK Spaces in Which the Sequence of Coordinate Vectors is Bounded

Published online by Cambridge University Press:  20 November 2018

William H. Ruckle
William H. Ruckle*
Affiliation:
Clems on University, Clemson, South Carolina
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.

The work presented in this paper was initially motivated by the following question of A. Wilansky: “Is there a smallest FK-space E in which is bounded?” Here FK-space means a complete linear metric space of real or complex sequences x = (xi) upon which the coordinate functional x → xt are continuous for each i (see [10, p. 202]), and An FK-space need not be locally convex, and therein lies the difficulty of the problem since it is easy to see that l1 is the smallest locally convex FK-space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 973 - 978
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Garling, D. J. H., On symmetric sequence spaces, Proc. London Math. Soc. 16 (1966), 85-106- 2. Symmetric bases of locally convex spaces, Studia Math. 80 (1968), 163–181.Google Scholar
3. Jones, O. T. and Retherford, J. R., On similar bases in barrelled spaces, Proc. Amer. Math. Soc. 18 (1967), 677–680.Google Scholar
4. Köthe, G., Topological vector spaces. I (Springer, Berlin, 1970).Google Scholar
5. Köthe, G. and Toeplitz, O., Lineare Ràume mit unendlich vielen Koordinaten und Ringe unendlichen Matrizen, J. Reine Agnew. Math. 171 (1934), 193–226.Google Scholar
6. Ruckle, W., Symmetric coordinate spaces and symmetric bases, Can. J. Math. 19 (1967), 828–838.Google Scholar
7. Ruckle, W., On perfect symmetric BK-spaces, Math. Ann. 175 (1968), 121–126.Google Scholar
8. Ruckle, W., Topologies on sequence spaces (to appear in Pacific J. Math.).Google Scholar
9. Singer, J., Bases in Banach spaces. I (Springer, Berlin, 1970).Google Scholar
10. Wilansky, A., Functional analysis (Blaisdell, New York, 1964).Google Scholar
11. Gramsch, B., Die Klasse metrisher linearer Raume L(Φ), Math. Ann. 171 (1967), 61–78.Google Scholar
12. Nakano, H., Concave modulares, J. Math. Loc. Japan 5 (1953), 29–49.Google Scholar