Subspaces of the Bourgain-Delbaen space

• Autorzy: Richard Haydon
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

$ℓ^1$-predual; $ℒ^∞$-space; $ℓ^p$-space

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 139
• Numer: 3
• Strony: 275-293

Daty

wydano

2000

otrzymano

1999-03-29

Twórcy

autor

Richard Haydon

• Brasenose College, Oxford OX1 4AJ, U.K.

Bibliografia

• [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.
• [3] M. Boddington, On a certain class of recursively defined norms, in preparation.
• [4] J. Bourgain, New Classes of $ℒ^p$-Spaces, Lecture Notes in Math. 889, Springer, Berlin, 1981.
• [5] J. Bourgain and F. Delbaen, A class of special $ℒ^∞$-spaces, Acta Math. 145 (1980), 155-176.
• [6] G. Godefroy, N. J. Kalton and G. Lancien, Szlenk indices and uniform homeomorphisms, preprint.
• [7] P. Hájek, Smooth functions on $c_0$, Israel J. Math. 104 (1998), 17-28.
• [8] W. B. Johnson, A uniformly convex Banach space which contains no $ℓ_p$, Compositio Math. 29 (1974), 179-190.
• [9] W. B. Johnson, J. Lindenstrauss and G. Schechtman, Banach spaces determined by their uniform structures, Geom. Funct. Anal. 6 (1996), 430-470.
• [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.