S-Barrelled Topological Vector Spaces*
Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 221-227

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

N. Bourbaki [1] was the first to introduce the class of locally convex topological vector spaces called “espaces tonnelés” or “barrelled spaces.” These spaces have some of the important properties of Banach spaces and Fréchet spaces. Indeed, a generalized Banach-Steinhaus theorem is valid for them, although barrelled spaces are not necessarily metrizable. Extensive accounts of the properties of barrelled locally convex topological vector spaces are found in [5] and [8].
Snipes, Ray F. S-Barrelled Topological Vector Spaces*. Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 221-227. doi: 10.4153/CMB-1978-037-5
@article{10_4153_CMB_1978_037_5,
     author = {Snipes, Ray F.},
     title = {S-Barrelled {Topological} {Vector} {Spaces*}},
     journal = {Canadian mathematical bulletin},
     pages = {221--227},
     year = {1978},
     volume = {21},
     number = {2},
     doi = {10.4153/CMB-1978-037-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-037-5/}
}
TY  - JOUR
AU  - Snipes, Ray F.
TI  - S-Barrelled Topological Vector Spaces*
JO  - Canadian mathematical bulletin
PY  - 1978
SP  - 221
EP  - 227
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-037-5/
DO  - 10.4153/CMB-1978-037-5
ID  - 10_4153_CMB_1978_037_5
ER  - 
%0 Journal Article
%A Snipes, Ray F.
%T S-Barrelled Topological Vector Spaces*
%J Canadian mathematical bulletin
%D 1978
%P 221-227
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-037-5/
%R 10.4153/CMB-1978-037-5
%F 10_4153_CMB_1978_037_5

[1] 1. Bourbaki, N., Sur Certains Espaces Vectoriels Topologiques. Ann. Inst. Fourier 2 (1950), pp. 5-16. Google Scholar

[2] 2. Dieudonn, J.é, and Schwartz, L., La Dualité dans les Espaces et (). Ann. Inst. Fourier 1 (1949), pp. 61-101. Google Scholar

[3] 3. Dudley, R. M., On Sequential Convergence. Trans. Amer. Math. Soc. 112 (1964), pp. 483-507. Google Scholar

[4] 4. Garsoux, J., Espaces Vectoriels Topologiques et Distributions. Dunod, Paris, 1963. Google Scholar

[5] 5. Horváth, J., Topological Vector Spaces and Distributions. Addison-Wesley, Reading (Mass.), 1966. Google Scholar

[6] 6. Husain, T., and Khaleelulla, S. M., On Countably, σ-, and Sequentially Barrelled Spaces. Canad. Math. Bull. 18 (1975), pp. 431-432. Google Scholar

[7] 7. Husain, T., and Yau-Chuen Wong, On Various Types of Barrelledness and the Hereditary Property of (DF)-Spaces. Glasgow Math. J. 17 (1976), pp. 134-143. Google Scholar

[8] 8. K, G.öthe, Topological Vector Spaces I. Springer-Verlag, New York, 1969. Google Scholar

[9] 9. Lohman, R. H., Convergence of Sequences in Fréchet Spaces. Boll. Un. Mat. Ital. (4) 4 (1971), pp. 345-350. Google Scholar

[10] 10. Schaefer, H. H., Topological Vector Spaces. Macmillan, New York, 1966. Google Scholar

[11] 11. Shirai, T., Sur les Topologies des Espaces de L. Schwartz. Proc. Jap. Acad. 35 (1959), pp. 31-36. Google Scholar

[12] 12. Snipes, R. F., C-Sequential and S-Bomological Topological Vector Spaces. Math. Ann. 202 (1973), pp. 273-283. Google Scholar

[13] 13. Webb, J. H., Sequential Convergence in Locally Convex Spaces. Proc. Camb. Phil. Soc. 64 (1968), pp. 341-364. Google Scholar

[14] 14. Wilansky, A., Functional Analysis. Blaisdell, New York, 1964. Google Scholar

[15] 15. Wilansky, A., Topics in Functional Analysis. Springer-Verlag, New York, 1967. Google Scholar

Cité par Sources :