The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices

D. R. Lewis

Compositio Mathematica (1983)

  • Volume: 50, Issue: 1, page 83-92
  • ISSN: 0010-437X

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Lewis, D. R.. "The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices." Compositio Mathematica 50.1 (1983): 83-92. <http://eudml.org/doc/89620>.

@article{Lewis1983,
author = {Lewis, D. R.},
journal = {Compositio Mathematica},
keywords = {complemented Hilbertian subspaces; uniformly convex Banach lattices; Hilbertian subspace; Banach lattice; Dvoretzky's theorem; uniformly complemented},
language = {eng},
number = {1},
pages = {83-92},
publisher = {Martinus Nijhoff Publishers},
title = {The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices},
url = {http://eudml.org/doc/89620},
volume = {50},
year = {1983},
}

TY - JOUR
AU - Lewis, D. R.
TI - The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 50
IS - 1
SP - 83
EP - 92
LA - eng
KW - complemented Hilbertian subspaces; uniformly convex Banach lattices; Hilbertian subspace; Banach lattice; Dvoretzky's theorem; uniformly complemented
UR - http://eudml.org/doc/89620
ER -

References

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  2. [2] T. Figiel, J. Lindenstrauss and V. Milman: The dimensions of almost spherical sections of convex bodies. Acta Math. 139 (1977) 53-94. Zbl0375.52002MR445274
  3. [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. Zbl0212.14203MR412775
  4. [4] Y. Gordon: On p-absolutely summing constants of Banach spaces. Israel J. Math.7 (1969) 151-163. Zbl0179.17502MR250028
  5. [5] Y. Gordon, D.R. Lewis and J.R. Retherford: Banach ideals of operators with applications. J. Func. Anal.14 (1973) 85-129. Zbl0272.47024MR380488
  6. [6] Y. Gordon and D.R. Lewis: Absolutely summing operators and local unconditional structure. Acta Math. 133 (1974) 27-48. Zbl0291.47017MR410341
  7. [7] F. John: Extremum problems with inequalities as subsidiary conditions. Courant Anniversity Volume, Interscience, New York, 1948, 187-204. Zbl0034.10503MR30135
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  11. [11] D.R. Lewis and Nicole Tomczak-Jaegermann: Hilbertian and complemented finite dimensional subspaces of Banach lattices and unitary ideals. Zbl0422.46019
  12. [12] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Volume II, Functions Spaces. Zbl0852.46015
  13. [13] B. Maurey, Type et cotype dans les espaces munis de structures locales inconditionnelles. Seminaire Maurey-Schwartz, 1973-1974, Exposes XXIV et XXV. Zbl0321.46013MR399796
  14. [14] B. Maurey, Un theoreme de prolongement. C.R. Acad. Sci. Paris279 (1974) 329-332. Zbl0291.47001MR355539
  15. [15] B. Maurey, Theoremes de factorisation pour les operators lineaires a valeurs dans les espaces LP. Asterisque 11, Societe Mathematique de France, 1974. Zbl0278.46028MR344931
  16. [16] A. Pelczynski and H.P. Rosenthal, Localization techniques in LP-spaces. Studia Math. 52 (1974) 263-289. Zbl0297.46023MR361729
  17. [17] A. Pietsch, Absolut p-summievende Abbiblungen in normierten Raumen, Studia Math. 28 (1966) 333-352. Zbl0156.37903MR216328
  18. [18] G. Pisier, Embedding spaces of operators into certain Banach lattices. The Altgeld Book, 1976, University of Illinois. 
  19. [19] Nicole Tomczak-Jaegermann, Finite dimensional subspaces of uniformly convex and uniformly smooth Banach lattices and trace class Sp, to appear Studia Math. Zbl0456.46019MR579732
  20. [20] Y. Benyamini and Y. Gordon: Random factorizations of operators between Banach spaces, to appear. Zbl0474.47010MR632456
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  22. [22] G. Pisier, to appear. MR1402756

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