On nearly euclidean decomposition for some classes of Banach spaces

Stanisłlaw Szarek; Nicole Tomczak-Jaegermann

Compositio Mathematica (1980)

  • Volume: 40, Issue: 3, page 367-385
  • ISSN: 0010-437X

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Szarek, Stanisłlaw, and Tomczak-Jaegermann, Nicole. "On nearly euclidean decomposition for some classes of Banach spaces." Compositio Mathematica 40.3 (1980): 367-385. <http://eudml.org/doc/89443>.

@article{Szarek1980,
author = {Szarek, Stanisłlaw, Tomczak-Jaegermann, Nicole},
journal = {Compositio Mathematica},
keywords = {large Euclidean subspaces; Euclidean decompositions; volume estimates; volume ratio; Banach-Mazur distance; cotype 2; unconditional basis},
language = {eng},
number = {3},
pages = {367-385},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {On nearly euclidean decomposition for some classes of Banach spaces},
url = {http://eudml.org/doc/89443},
volume = {40},
year = {1980},
}

TY - JOUR
AU - Szarek, Stanisłlaw
AU - Tomczak-Jaegermann, Nicole
TI - On nearly euclidean decomposition for some classes of Banach spaces
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 40
IS - 3
SP - 367
EP - 385
LA - eng
KW - large Euclidean subspaces; Euclidean decompositions; volume estimates; volume ratio; Banach-Mazur distance; cotype 2; unconditional basis
UR - http://eudml.org/doc/89443
ER -

References

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  1. [1] T. Figiel: On the moduli of convexity and smoothness. Studia Math.56 (1976) 121-155. Zbl0344.46052MR425581
  2. [2] T. Figiel, J. Lindenstrauss and V.D. Milman: On dimension of almost spherical sections of convex bodies. Acta Math.139 (1977) 53-94. Zbl0375.52002MR445274
  3. [3] I.C. Gohberg and M.G. Krein: Introduction to the theory of linear nonselfadjoint operators, Moskwa1965 (in Russian). American translation AMS Translations, Vol. 18. Zbl0181.13504
  4. [4] R.I. Jamison and W.H. Ruckel: Factoring absolutely convergent series. Math. Ann.224 (1976) 143-148. Zbl0319.40007MR435791
  5. [5] F. John: Extremum problems with inequalities as subsidiary conditions, Courant Anniversary volume, Interscience, New York1948, pp. 187-204. Zbl0034.10503MR30135
  6. [6] W.B. Johnson, B. Maurey, G. Schechrman and L. Tzafriri (in preparation). 
  7. [7] B.S. Kashin: The order of diameters of some classes of smooth functions. Uspiehi Mat. Nauk32 (1977) 191-192 (in Russian). 
  8. [8] J. Lindenstrauss and L. Tzafriri: Classical Banach spaces, Lecture Notes in Math.Berlin- Heidelberg-New York, Springer1973. Zbl0259.46011MR415253
  9. [9] B. Maurey: Un théorème de prolongement, C.R. Acad. Sci. Paris, Sér A-B, 279 (1974) 329-332. Zbl0291.47001MR355539
  10. [10] B. Maurey and G. Pisier: Series de variable aléatoires vectori rielles independantes et propriétés geometriques des espaces de Banach, Studia Math.58 (1976) 45-90. Zbl0344.47014MR443015
  11. [11] S.J. Szarek: On Kashin's almost Euclidean orthogonal decomposition of lnl (to appear in Bull. Acad. Sci. Polon). Zbl0395.46015

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