The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices
Lewis, D. R.
Compositio Mathematica, Tome 50 (1983), p. 83-92 / Harvested from Numdam
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Publié le : 1983-01-01
@article{CM_1983__50_1_83_0,
     author = {Lewis, D. R.},
     title = {The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices},
     journal = {Compositio Mathematica},
     volume = {50},
     year = {1983},
     pages = {83-92},
     mrnumber = {719068},
     zbl = {0531.46017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1983__50_1_83_0}
}

Lewis, D. R. The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices. Compositio Mathematica, Tome 50 (1983) pp. 83-92. http://gdmltest.u-ga.fr/item/CM_1983__50_1_83_0/

[1] A. Dvoretzky: Some results on convex bodies and Banach spaces. Proc. Int. Symp. on Linear Spaces. Jerusalem, 1961, 123-160. | MR 139079 | Zbl 0119.31803

[2] T. Figiel, J. Lindenstrauss and V. Milman: The dimensions of almost spherical sections of convex bodies. Acta Math. 139 (1977) 53-94. | MR 445274 | Zbl 0375.52002

[3] D.J.H. Garling and Y. Gordon: Relations between some constants associated with finite-dimensional Banach spaces. Israel J. Math. 9 (1971) 346-361. | MR 412775 | Zbl 0212.14203

[4] Y. Gordon: On p-absolutely summing constants of Banach spaces. Israel J. Math. 7 (1969) 151-163. | MR 250028 | Zbl 0179.17502

[5] Y. Gordon, D.R. Lewis and J.R. Retherford: Banach ideals of operators with applications. J. Func. Anal. 14 (1973) 85-129. | MR 380488 | Zbl 0272.47024

[6] Y. Gordon and D.R. Lewis: Absolutely summing operators and local unconditional structure. Acta Math. 133 (1974) 27-48. | MR 410341 | Zbl 0291.47017

[7] F. John: Extremum problems with inequalities as subsidiary conditions. Courant Anniversity Volume, Interscience, New York, 1948, 187-204. | MR 30135 | Zbl 0034.10503

[8] W.B. Johnson, and L. Tzafriri: On the local structure of subspaces of Banach lattices. Israel J. Math. 20 (1975) 292-299. | MR 420210 | Zbl 0311.46003

[9] J.L. Krivine, Theoremes des factorisation dans les espaces reticules. Seminaire Maurey-Schwartz, 1973 -1974, Exposes No. XXII et XXIII. | Numdam | MR 440334 | Zbl 0295.47024

[10] D.R. Lewis, Ellipsoids defined by Banach ideal norms, to appear in Mathematika. | MR 557122 | Zbl 0438.46006

[11] D.R. Lewis and Nicole Tomczak-Jaegermann: Hilbertian and complemented finite dimensional subspaces of Banach lattices and unitary ideals. | Zbl 0422.46019

[12] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Volume II, Functions Spaces. | Zbl 0852.46015

[13] B. Maurey, Type et cotype dans les espaces munis de structures locales inconditionnelles. Seminaire Maurey-Schwartz, 1973-1974, Exposes XXIV et XXV. | Numdam | MR 399796 | Zbl 0321.46013

[14] B. Maurey, Un theoreme de prolongement. C.R. Acad. Sci. Paris 279 (1974) 329-332. | MR 355539 | Zbl 0291.47001

[15] B. Maurey, Theoremes de factorisation pour les operators lineaires a valeurs dans les espaces LP. Asterisque 11, Societe Mathematique de France, 1974. | MR 344931 | Zbl 0278.46028

[16] A. Pelczynski and H.P. Rosenthal, Localization techniques in LP-spaces. Studia Math. 52 (1974) 263-289. | MR 361729 | Zbl 0297.46023

[17] A. Pietsch, Absolut p-summievende Abbiblungen in normierten Raumen, Studia Math. 28 (1966) 333-352. | MR 216328 | Zbl 0156.37903

[18] G. Pisier, Embedding spaces of operators into certain Banach lattices. The Altgeld Book, 1976, University of Illinois.

[19] Nicole Tomczak-Jaegermann, Finite dimensional subspaces of uniformly convex and uniformly smooth Banach lattices and trace class Sp, to appear Studia Math. | MR 579732 | Zbl 0456.46019

[20] Y. Benyamini and Y. Gordon: Random factorizations of operators between Banach spaces, to appear. | MR 632456 | Zbl 0474.47010

[21] T. Figiel and Nicole Tomczak-Jaegermann: Projections onto Hilbertian subspaces of Banach spaces, to appear. | MR 571251 | Zbl 0427.46010

[22] G. Pisier, to appear. | MR 1402756