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Inclusion Theorems for K-Spaces

Published online by Cambridge University Press:  20 November 2018

G. Bennett  and
N. J. Kalton
G. Bennett
Affiliation:
Indiana University, Bloomington, Indiana
N. J. Kalton
Affiliation:
University College of Swansea, Swansea, Wales
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A sequence space is a vector subspace of the space ω of all real (or complex) sequences. A sequence space E with a locally convex topology τ is called a K- space if the inclusion map E → ω is continuous, when ω is endowed with the product topology . A K-space E with a Frechet (i.e., complete, metrizable and locally convex) topology is called an FK-space; if the topology is a Banach topology, then E is called a BK-space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 511 - 524
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bachelis, G. F. and Rosenthal, H. P., On unconditionally converging series and biorthogonal systems in a Banach space, Pacific J. Math. 37 (1971), 1–5.Google Scholar
2. Bennett, G., A representation theorem for summability domains, Proc. London Math. Soc. 24 ((1972), 193–203.Google Scholar
3. Bennett, G., A new class of sequence spaces with applications in summability theory, J. Reine Agnew. Math, (to appear).Google Scholar
4. Bennett, G. and Cooper, J. B., Weak bases in (F)- and (LF)-spaces, J. London Math. Soc. 44 (1969), 505–508.Google Scholar
5. Bennett, G. and Kalton, N. J., FK-spaces containing cQ, Duke Math. J. 55 (1972), 561–582.Google Scholar
6. Garling, D. J. H., On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 997–1019.Google Scholar
7. Garling, D. J. H., The β- and γ-duality of sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 963–981.Google Scholar
8. Hayman, W. K., Interpolation by bounded functions, Ann. Inst. Fourier (Grenoble) 8 (1958), 277–290.Google Scholar
9. Hoffman, K., Banach spaces of analytic functions (Prentice-Hall, New Jersey, 1967).Google Scholar
10. Kadec, M. I. and Pelczynski, A., Basic sequences, biorthogonal sequences and norming sets in Banach and Frechet spaces, Studia Math. 25 (1965), 297–323 (Russian).Google Scholar
11. Kalton, N. J., Some forms of the closed graph theorem, Proc. Cambridge Philos. Soc. 70 (1971), 401–408.Google Scholar
12. Köthe, G., Topological vector spaces. I (Springer, New York, 1969).Google Scholar
13. Kwapien, S., Some remarks on (p, q) absolutely summing operators in lp spaces, Studia Math. 29 (1968), 327–336.Google Scholar
14. Lindenstrauss, J. and Pelczynski, A., Absolutely summing operators inL spaces T. and their applications, Studia Math. 29 (1968), 275–326.Google Scholar
15. Littlewood, J. E., On bounded bilinear forms in an infinite number of variables, Quart. Jour. Math. Oxford Ser. 1 (1930), 164–174.Google Scholar
16. Lorentz, G. G., Direct theorems on methods of summability. II, Can. J. Math. 3 (1951), 236–256.Google Scholar
17. Mahowald, M., Barrelled spaces and the closed graph theorem, J. London Math. Soc. 36 (1961), 108–110.Google Scholar
18. Mazur, S. and Orlicz, W., On linear methods of summability, Studia Math. 14 (1955), 129–160.Google Scholar
19. Pelczynski, A. et Szlenk, W., Sur Vinjection naturelle de Vespace l dans l'espace lp f Colloq. Math. 10 (1963), 313–323.Google Scholar
20. Peyerimhoff, A., Über ein Lemma von Herrn H. C. Chow, J. London Math. Soc. 32 (1957), 33–36.Google Scholar
21. Robertson, A. P. and Robertson, W. J., Topological vector spaces (Cambridge University Press, Cambridge, 1964).Google Scholar
22. Sargent, W. L. C., Some sequence spaces related to the ft spaces, J. London Math. Soc. 35 (1960), 161–171.Google Scholar
23. Schaefer, H. H., Topological vector spaces (Macmillan, New York, 1966).Google Scholar
24. Seever, G., Measures on F-spaces, Trans. Amer. Math. Soc. 133 (1968), 267–280.Google Scholar
25. Shields, A., Review of [81, Math. Reviews 22 (1961), #8128.Google Scholar
26. Snyder, A. K., Sequence spaces and interpolation problems for analytic functions, Studia Math. 39 (1971), 137–153.Google Scholar
27. Tong, A. E., Diagonal submatrices of matrix maps, Pacific J. Math. 32 (1970), 551–559.Google Scholar
28. Webb, J. H., Sequential convergence in locally convex spaces, Proc. Cambridge Philos. Soc. 64 (1968), 341–364.Google Scholar
29. Zeller, K., Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463–487.Google Scholar
30. Zeller, K., Matrixtransformationen von Folgenraumen, Univ. Roma. 1st. Naz. Alta. Mat. Rend. Mat. e Appl. (5) 12 (1954), 340–346.Google Scholar