A factorization theorem in Banach lattices and its application to Lorentz spaces
Annales de l'Institut Fourier, Volume 31 (1981) no. 1, p. 239-255

p-convexity and q-concavity of a Banach lattice L are characterized by factorization of multiplication operators from L q into L p through L. This characterization is applied to calculate the concavity type of Lorentz spaces.

On caractérise la p-convexité et la q-concavité d’un treillis de Banach L à l’aide de la factorisation des opérateurs de multiplication de L q dans L p à travers l’espace L. Cette caractérisation est utilisée pour calculer le type de concavité des espace de Lorentz.

@article{AIF_1981__31_1_239_0,
     author = {Reisner, Sholomo},
     title = {A factorization theorem in Banach lattices and its application to Lorentz spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {31},
     number = {1},
     year = {1981},
     pages = {239-255},
     doi = {10.5802/aif.825},
     zbl = {0437.46025},
     mrnumber = {82g:46066},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1981__31_1_239_0}
}
Reisner, Sholomo. A factorization theorem in Banach lattices and its application to Lorentz spaces. Annales de l'Institut Fourier, Volume 31 (1981) no. 1, pp. 239-255. doi : 10.5802/aif.825. http://www.numdam.org/item/AIF_1981__31_1_239_0/

[1] Z. Altshuler, Uniform convexity in Lorentz sequence spaces, Israel J. Math., 20 (1975), 260-274. | MR 52 #6378 | Zbl 0309.46007

[2] A.P. Calderon, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113-190. | MR 29 #5097 | Zbl 0204.13703

[3] T. Figiel, W.B. Johnson and L. Tzafriri, On Banach lattices and spaces having local unconditional structure, with applications to Lorentz function spaces, J. Approx. Th., 13 (1975), 395-412. | MR 51 #3866 | Zbl 0307.46007

[4] I. Halperin, Uniform convexity in function spaces, Canadian J. Math., 21 (1954), 195-204. | MR 15,880b | Zbl 0055.33702

[5] R.E. Jamison and W.H. Ruckle, Factoring absolutely convergent series, Math. Ann., 227 (1976), 143-148. | MR 55 #8747 | Zbl 0319.40007

[6] J.L. Krivine, Théorèmes de factorisation dans les espaces réticulés, Séminaire Maurey-Schwartz, 1973-1974, Exp. 12-13. | Numdam

[7] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, parts I and II, Springer Verlag, 1979. | MR 81c:46001 | Zbl 0403.46022

[8] G.G. Lorentz, On the theory of spaces Λ, Pacific J. Math., 1 (1951), 411-429. | MR 13,470c | Zbl 0043.11302

[9] G.Y. Lozanovskii, On some Banach lattices, Siberian Math. J., 10 (1969), 419-430. | Zbl 0194.43302

[10] G. Pisier, Some applications of the complex interpolation method to Banach lattices, J. D'Analyse Math., 35 (1979), 264-280. | MR 80m:46020 | Zbl 0427.46048