Inclusion Theorems for K-Spaces
Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 511-524

Voir la notice de l'article provenant de la source Cambridge University Press

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.
Bennett, G.; Kalton, N. J. Inclusion Theorems for K-Spaces. Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 511-524. doi: 10.4153/CJM-1973-052-2
@article{10_4153_CJM_1973_052_2,
     author = {Bennett, G. and Kalton, N. J.},
     title = {Inclusion {Theorems} for {K-Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {511--524},
     year = {1973},
     volume = {25},
     number = {3},
     doi = {10.4153/CJM-1973-052-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1973-052-2/}
}
TY  - JOUR
AU  - Bennett, G.
AU  - Kalton, N. J.
TI  - Inclusion Theorems for K-Spaces
JO  - Canadian journal of mathematics
PY  - 1973
SP  - 511
EP  - 524
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1973-052-2/
DO  - 10.4153/CJM-1973-052-2
ID  - 10_4153_CJM_1973_052_2
ER  - 
%0 Journal Article
%A Bennett, G.
%A Kalton, N. J.
%T Inclusion Theorems for K-Spaces
%J Canadian journal of mathematics
%D 1973
%P 511-524
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1973-052-2/
%R 10.4153/CJM-1973-052-2
%F 10_4153_CJM_1973_052_2

[1] 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] 2. Bennett, G., A representation theorem for summability domains, Proc. London Math. Soc. 24 ((1972), 193–203. Google Scholar

[3] 3. Bennett, G., A new class of sequence spaces with applications in summability theory, J. Reine Agnew. Math, (to appear). Google Scholar

[4] 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] 5. Bennett, G. and Kalton, N. J., FK-spaces containing cQ, Duke Math. J. 55 (1972), 561–582. Google Scholar

[6] 6. Garling, D. J. H., On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 997–1019. Google Scholar

[7] 7. Garling, D. J. H., The β- and γ-duality of sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 963–981. Google Scholar

[8] 8. Hayman, W. K., Interpolation by bounded functions, Ann. Inst. Fourier (Grenoble) 8 (1958), 277–290. Google Scholar

[9] 9. Hoffman, K., Banach spaces of analytic functions (Prentice-Hall, New Jersey, 1967). Google Scholar

[10] 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] 11. Kalton, N. J., Some forms of the closed graph theorem, Proc. Cambridge Philos. Soc. 70 (1971), 401–408. Google Scholar

[12] 12. Köthe, G., Topological vector spaces. I (Springer, New York, 1969). Google Scholar

[13] 13. Kwapien, S., Some remarks on (p, q) absolutely summing operators in lp spaces, Studia Math. 29 (1968), 327–336. Google Scholar

[14] 14. Lindenstrauss, J. and Pelczynski, A., Absolutely summing operators inL spaces T. and their applications, Studia Math. 29 (1968), 275–326. Google Scholar

[15] 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] 16. Lorentz, G. G., Direct theorems on methods of summability. II, Can. J. Math. 3 (1951), 236–256. Google Scholar

[17] 17. Mahowald, M., Barrelled spaces and the closed graph theorem, J. London Math. Soc. 36 (1961), 108–110. Google Scholar

[18] 18. Mazur, S. and Orlicz, W., On linear methods of summability, Studia Math. 14 (1955), 129–160. Google Scholar

[19] 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] 20. Peyerimhoff, A., Über ein Lemma von Herrn H. C. Chow, J. London Math. Soc. 32 (1957), 33–36. Google Scholar

[21] 21. Robertson, A. P. and Robertson, W. J., Topological vector spaces (Cambridge University Press, Cambridge, 1964). Google Scholar

[22] 22. Sargent, W. L. C., Some sequence spaces related to the ft spaces, J. London Math. Soc. 35 (1960), 161–171. Google Scholar

[23] 23. Schaefer, H. H., Topological vector spaces (Macmillan, New York, 1966). Google Scholar

[24] 24. Seever, G., Measures on F-spaces, Trans. Amer. Math. Soc. 133 (1968), 267–280. Google Scholar

[25] 25. Shields, A., Review of [81, Math. Reviews 22 (1961), #8128. Google Scholar

[26] 26. Snyder, A. K., Sequence spaces and interpolation problems for analytic functions, Studia Math. 39 (1971), 137–153. Google Scholar

[27] 27. Tong, A. E., Diagonal submatrices of matrix maps, Pacific J. Math. 32 (1970), 551–559. Google Scholar

[28] 28. Webb, J. H., Sequential convergence in locally convex spaces, Proc. Cambridge Philos. Soc. 64 (1968), 341–364. Google Scholar

[29] 29. Zeller, K., Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463–487. Google Scholar

[30] 30. Zeller, K., Matrixtransformationen von Folgenraumen, Univ. Roma. 1st. Naz. Alta. Mat. Rend. Mat. e Appl. (5) 12 (1954), 340–346. Google Scholar

Cité par Sources :