# Subspaces of the Bourgain-Delbaen space

Studia Mathematica (2000)

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

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topHaydon, 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

top- [1] D. Alspach, The dual of the Bourgain-Delbaen space, preprint, Oklahoma State Univ., 1998.
- [2] S. M. Bates, On smooth non-linear surjections of Banach spaces, Israel J. Math. 100 (1997), 209-220. Zbl0898.46044
- [3] M. Boddington, On a certain class of recursively defined norms, in preparation.
- [4] J. Bourgain, New Classes of ${\mathcal{L}}^{p}$-Spaces, Lecture Notes in Math. 889, Springer, Berlin, 1981.
- [5] J. Bourgain and F. Delbaen, A class of special ${\mathcal{L}}^{\infty}$-spaces, Acta Math. 145 (1980), 155-176. Zbl0466.46024
- [6] G. Godefroy, N. J. Kalton and G. Lancien, Szlenk indices and uniform homeomorphisms, preprint. Zbl0981.46007
- [7] P. Hájek, Smooth functions on ${c}_{0}$, Israel J. Math. 104 (1998), 17-28. Zbl0940.46023
- [8] W. B. Johnson, A uniformly convex Banach space which contains no ${\ell}_{p}$, Compositio Math. 29 (1974), 179-190. Zbl0301.46013
- [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] 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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