Geodesic
Some isometric characterizations of ln∞
Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 117-121

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

The previous results on isometrically characterizing ln∞ in terms of operator ideal norms can be summarized as follows.Let E be an n-dimensional Banach space.(1) If λ(E) = 1, then (see [3], [5], [6]), where λ(E) is the projection constant of E (see [4]).(2) If π(E) = n, then (see [1],[2]).(3) If Δ2(E) = √n, then (see [8]), where Δ2(E) is the 2-dominated constant of E(see [4]).(4) If for any linear operator T: → E, v1(T) = (T), then (see [7]), where v1 is the 1-nuclear norm (see [4]). 
Zhu, Jiang. Some isometric characterizations of ln∞. Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 117-121. doi: 10.1017/S0017089500008600
@article{10_1017_S0017089500008600,
     author = {Zhu, Jiang},
     title = {Some isometric characterizations of ln\ensuremath{\infty}},
     journal = {Glasgow mathematical journal},
     pages = {117--121},
     year = {1992},
     volume = {34},
     number = {1},
     doi = {10.1017/S0017089500008600},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008600/}
}
TY  - JOUR
AU  - Zhu, Jiang
TI  - Some isometric characterizations of ln∞
JO  - Glasgow mathematical journal
PY  - 1992
SP  - 117
EP  - 121
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008600/
DO  - 10.1017/S0017089500008600
ID  - 10_1017_S0017089500008600
ER  - 
%0 Journal Article
%A Zhu, Jiang
%T Some isometric characterizations of ln∞
%J Glasgow mathematical journal
%D 1992
%P 117-121
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008600/
%R 10.1017/S0017089500008600
%F 10_1017_S0017089500008600

[1] 1.Deschaseaux, J. P., Une caractérisation de certains espaces vectoriels normés de dimension finie par leur constante de Macphail, C. R. Acad. Sci. Paris Sér. A–B 276 (1973), A1349–A1351. Google Scholar

[2] 2.Garling, D. J. H., Operators with large trace, and a characterization of l n, Proc. Cambridge Philos. Soc. 76 (1974), 413–414. Google Scholar | DOI

[3] 3.Goodner, D. B., Projections on normed linear spaces, Trans. Amer. Math. Soc. 69 (1950), 89–108. Google Scholar | DOI

[4] 4.Jameson, G. J. O., Summing and nuclear norms in Banach space theory (Cambridge University Press, 1987). Google Scholar | DOI

[5] 5.Kelley, J. L., Banach spaces with the extension property, Trans. Amer. Math. Soc. 72 (1952), 323–326. Google Scholar | DOI

[6] 6.Nachbin, L., A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28–46. Google Scholar | DOI

[7] 7.Pelczynski, A. and Tomczak-Jaegermann, N., On the length of faithful nuclear representation of finite rank operators, Mathematika 35 (1988), 126–134. Google Scholar | DOI

[8] 8.Tomczak-Jaegermann, N., Banach-Mazur distances and finite-dimensional operator ideals (Pitman, 1988). Google Scholar

Cité par Sources :