Geodesic
Banach Envelopes of Non-Locally Convex Spaces
Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 65-86

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

Let X be a quasi-Banach space whose dual X* separates the points of X. Then X* is a Banach space under the norm From X we can construct the Banach envelope Xc of X by defining for x ∊ X, the norm Then Xc is the completion of (X, ‖ ‖c ). Alternatively ‖ ‖c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X → Z into a Banach space extends with preservation of norm to an operator . 
Kalton, N. J. Banach Envelopes of Non-Locally Convex Spaces. Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 65-86. doi: 10.4153/CJM-1986-004-2
@article{10_4153_CJM_1986_004_2,
     author = {Kalton, N. J.},
     title = {Banach {Envelopes} of {Non-Locally} {Convex} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {65--86},
     year = {1986},
     volume = {38},
     number = {1},
     doi = {10.4153/CJM-1986-004-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-004-2/}
}
TY  - JOUR
AU  - Kalton, N. J.
TI  - Banach Envelopes of Non-Locally Convex Spaces
JO  - Canadian journal of mathematics
PY  - 1986
SP  - 65
EP  - 86
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-004-2/
DO  - 10.4153/CJM-1986-004-2
ID  - 10_4153_CJM_1986_004_2
ER  - 
%0 Journal Article
%A Kalton, N. J.
%T Banach Envelopes of Non-Locally Convex Spaces
%J Canadian journal of mathematics
%D 1986
%P 65-86
%V 38
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-004-2/
%R 10.4153/CJM-1986-004-2
%F 10_4153_CJM_1986_004_2

[1] 1. Bennett, G., An extension of the Riesz-Thorin theorem, 1–13 in Banach spaces of analytic functions (Springer Lecture Notes 604, New York, 1977). Google Scholar | DOI

[2] 2. Bennett, G., Lectures on matrix transformations of lp spaces, 36–80 in Notes on Banach spaces (University of Texas Press, Austin, Texas, 1980). Google Scholar

[3] 3. Duren, P. L., Romberg, B. W. and Shields, A L., Linear functional on Hp spaces with 0 < p < 1, J. Reine Angew. Math. 38 (1969), 32–60. Google Scholar

[4] 4. James, R. C., A nonreflexive Banach space that is uniformly nonoctahedral, Israel J. Math. 18 (1974), 145–155. Google Scholar

[5] 5. Kalton, N. J., The three space problem for locally bounded F-spaces, Comp. Math 37 (1978), 243–276. Google Scholar

[6] 6. Kalton, N. J., Convexity conditions for non-locally convex lattices, Glasgow Math. J. 25 (1984), 141–152. Google Scholar

[7] 7. Lindenstrauss, J. and Pelczynski, A., Absolutely summing operators in Lp-spaces and their applications, Studia Math. 29 (1968), 275–326. Google Scholar

[8] 8. Maurey, B., Théorèmes de factorisations pour les operateurs linéaires a valeurs dans les espaces L , Asterique 11 (1973). Google Scholar

[9] 9. Maurey, B., Quelques problèmes de factorisation d'operateurs linéaires, Proc. Int. Congress Math. Vancouver 1974, Vol. II (1975), 75–80. Google Scholar

[10] 10. Maurey, B. and Pisier, G., Series de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), 45–90. Google Scholar

[11] 11. Pelczynski, A., All separable Banach spaces admit for every fundamental and total biorthogonal systems bounded by , Studia Math. 55 (1976), 295–304. Google Scholar

[12] 12. Pisier, G., Sur les espaces de Banach qui ne contient pas uniformément de , C. R. Acad. Sci (Paris) 277 (1973), 991–994. Google Scholar

[13] 13. Rolewicz, S., Metric linear spaces (Monografie Matematyczne 56, PWN, Warsaw, 1972). Google Scholar

[14] 14. Shapiro, J. H., Mackey topologies, reproducing kernels and diagonal maps on Hardy and Bergman spaces, Duke Math. J. 43 (1976), 187–202. Google Scholar

[15] 15. Shapiro, J. H., Linear topological properties of the harmonic Hardy spaces h for 0 < p < 1, Illinois J. Math, to appear. Google Scholar

[16] 16. Talagrand, M., A simple example of a pathological submeasure, Math. Ann. 252 (1980), 97–102. Google Scholar

[17] 17. Wojtasczyk, P., On projections and unconditional bases in direct sums of Banach spaces II Studia Math. 62 (1978), 193–201. Google Scholar

[18] 18. Wojtasczyk, P., Hp spaces, p ≦ 1 and spline systems, Studia Math. 77 (1984), 289–320. Google Scholar

Cité par Sources :