Subspaces of the Bourgain-Delbaen space

Richard Haydon

Studia Mathematica (2000)

  • Volume: 139, Issue: 3, page 275-293
  • ISSN: 0039-3223

Abstract

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It is shown that every infinite-dimensional closed subspace of the Bourgain-Delbaen space X a , b has a subspace isomorphic to some ℓ p .

How to cite

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Haydon, Richard. "Subspaces of the Bourgain-Delbaen space." Studia Mathematica 139.3 (2000): 275-293. <http://eudml.org/doc/216723>.

@article{Haydon2000,
abstract = {It is shown that every infinite-dimensional closed subspace of the Bourgain-Delbaen space $X_\{a,b\}$ has a subspace isomorphic to some $ℓ^p$.},
author = {Haydon, Richard},
journal = {Studia Mathematica},
keywords = {$ℓ^1$-predual; $ℒ^∞$-space; $ℓ^p$-space; Bourgain-Delbaen space; separable -spaces; Radon-Nikodým property; unconditional basic sequence},
language = {eng},
number = {3},
pages = {275-293},
title = {Subspaces of the Bourgain-Delbaen space},
url = {http://eudml.org/doc/216723},
volume = {139},
year = {2000},
}

TY - JOUR
AU - Haydon, Richard
TI - Subspaces of the Bourgain-Delbaen space
JO - Studia Mathematica
PY - 2000
VL - 139
IS - 3
SP - 275
EP - 293
AB - It is shown that every infinite-dimensional closed subspace of the Bourgain-Delbaen space $X_{a,b}$ has a subspace isomorphic to some $ℓ^p$.
LA - eng
KW - $ℓ^1$-predual; $ℒ^∞$-space; $ℓ^p$-space; Bourgain-Delbaen space; separable -spaces; Radon-Nikodým property; unconditional basic sequence
UR - http://eudml.org/doc/216723
ER -

References

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  1. [1] D. Alspach, The dual of the Bourgain-Delbaen space, preprint, Oklahoma State Univ., 1998. 
  2. [2] S. M. Bates, On smooth non-linear surjections of Banach spaces, Israel J. Math. 100 (1997), 209-220. Zbl0898.46044
  3. [3] M. Boddington, On a certain class of recursively defined norms, in preparation. 
  4. [4] J. Bourgain, New Classes of ℒ p -Spaces, Lecture Notes in Math. 889, Springer, Berlin, 1981. 
  5. [5] J. Bourgain and F. Delbaen, A class of special ℒ ∞ -spaces, Acta Math. 145 (1980), 155-176. Zbl0466.46024
  6. [6] G. Godefroy, N. J. Kalton and G. Lancien, Szlenk indices and uniform homeomorphisms, preprint. Zbl0981.46007
  7. [7] P. Hájek, Smooth functions on c 0 , Israel J. Math. 104 (1998), 17-28. Zbl0940.46023
  8. [8] W. B. Johnson, A uniformly convex Banach space which contains no ℓ p , Compositio Math. 29 (1974), 179-190. Zbl0301.46013
  9. [9] W. B. Johnson, J. Lindenstrauss and G. Schechtman, Banach spaces determined by their uniform structures, Geom. Funct. Anal. 6 (1996), 430-470. Zbl0864.46008
  10. [10] B. Maurey, V. Milman and N. Tomczak-Jaegermann, Asymptotic infinite-dimensional theory of Banach spaces, in: Oper. Theory Adv. Appl. 77, Birkhäuser, Basel, 1995, 149-175. Zbl0872.46013

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