Geodesic
Lorentz sequence spaces
Matematičeskie zametki, Tome 20 (1976) no. 4, pp. 501-510 
S. A. Rakov. Lorentz sequence spaces. Matematičeskie zametki, Tome 20 (1976) no. 4, pp. 501-510. http://geodesic.mathdoc.fr/item/MZM_1976_20_4_a4/
@article{MZM_1976_20_4_a4,
     author = {S. A. Rakov},
     title = {Lorentz sequence spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {501--510},
     year = {1976},
     volume = {20},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_4_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the condition $$ \sup\limits_n\Bigl\{n^{1/2}\Bigl(\sum_{j\le n}c_j^2\Bigr)^{1/2}\Bigr/\sum_{j\le n}c_j\Bigr\}<\infty $$ on the normalizing sequence $\{c_j\}_{j<\infty}$ of the Lorentz sequence space $\Lambda(c)$ is a necessary and sufficient condition for having each bounded linear operator acting from an arbitrary $\mathscr L_\infty$-space into $\Lambda(c)$ be 2-absolutely summing.