Geodesic
Inclusion Theorems for FX-Spaces
Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 631-645

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

The main result of this paper is Theorem 1 (in connection with Corollary 1 (e)), which says that the implication * holds for every separable FK-space F, for every FK-space E containing φ and for certain (for example, solid) FK-AB-spaces Y. At this, φ denotes the space of all finite sequences and WE is the set of all elements of E being weakly sectionally convergent.This result was proved by Bennett and Kalton ([1] and [3]) in the special case that E contains all null sequences and that Y is the space m of all bounded sequences or the space of all sequences almost converging to zero. 
Boos, Johann. Inclusion Theorems for FX-Spaces. Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 631-645. doi: 10.4153/CJM-1987-031-9
@article{10_4153_CJM_1987_031_9,
     author = {Boos, Johann},
     title = {Inclusion {Theorems} for {FX-Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {631--645},
     year = {1987},
     volume = {39},
     number = {3},
     doi = {10.4153/CJM-1987-031-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-031-9/}
}
TY  - JOUR
AU  - Boos, Johann
TI  - Inclusion Theorems for FX-Spaces
JO  - Canadian journal of mathematics
PY  - 1987
SP  - 631
EP  - 645
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-031-9/
DO  - 10.4153/CJM-1987-031-9
ID  - 10_4153_CJM_1987_031_9
ER  - 
%0 Journal Article
%A Boos, Johann
%T Inclusion Theorems for FX-Spaces
%J Canadian journal of mathematics
%D 1987
%P 631-645
%V 39
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-031-9/
%R 10.4153/CJM-1987-031-9
%F 10_4153_CJM_1987_031_9

[1] 1. Bennett, G. and Kalton, N. J., FK-spaces containing c , Duke Math. J. 39 (1972), 561–582. Google Scholar

[2] 2. Bennett, G. and Kalton, N. J., Inclusion theorems for K-spaces, Can. J. Math. 25 (1973), 511–524. Google Scholar

[3] 3. Bennett, G. and Kalton, N. J., Consistency theorems for almost convergence, Trans Amer. Math. Soc. 198 (1974), 23–43. Google Scholar

[4] 4. Boos, J., Verträglichkeit von konvergenztreuen Matrixverfahren, Math. Z. 128 (1972), 15–22. Google Scholar

[5] 5. Boos, J. and Leiger, T., Sätze vom Mazur-Orlicz-Typ, Studia Math. 81 (1985), 71–85. Google Scholar

[6] 6. Brudno, A. L., Summation of bounded sequences by matrices, Math. Sbornik, n. Ser. 16 (1945), 191–247. Google Scholar

[7] 7. Duran, J. P., Infinite matrices and almost convergence, Math. Z. 128 (1972), 75–83. Google Scholar

[8] 8. Mazur, S. and Orlicz, W., Sur les méthodes linéaires de sommation, C. R. Acad. Sci. Paris 196 (1933), 32–34. Google Scholar

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

[10] 10. Snyder, A. K., Consistency theory in semiconservatice spaces, Studia Math. 71 (1982), 1–13. Google Scholar

[11] 11. Volkov, I. I., Über die Verträ;glichkeit zweier Summationsmethoden, Mat. Zametki 1 (1967), 283–290. Google Scholar

[12] 12. Wilansky, A., Distinguished subsets and summability invariants, J. Analyse Math. 12 (1964), 327–350. Google Scholar

[13] 13. Wilansky, A., Summability through functional analysis (Amsterdam-New York-Oxford: North Holland, 1984). Google Scholar

Cité par Sources :