Geodesic
Hereditary approximation property
W. B. Johnson1 ; A. Szankowski2
1 Department of Mathematics<br/> Texas A&M University<br/> College Station, TX 77843-3368
2 The Hebrew University of Jerusalem<br/>Jerusalem 91904<br/> Israel
Annals of mathematics, Tome 176 (2012) no. 3, pp. 1987-2001.

Voir la notice de l'article provenant de la source Annals of Mathematics website

If $X$ is a Banach space such that the isomorphism constant to $\ell_2^n$ from $n$-dimensional subspaces grows sufficiently slowly as $n\to \infty$, then $X$ has the approximation property. A consequence of this is that there is a Banach space $X$ with a symmetric basis but not isomorphic to $\ell_2$ so that all subspaces of $X$ have the approximation property. This answers a problem raised in 1980. An application of the main result is that there is a separable Banach space $X$ that is not isomorphic to a Hilbert space, yet every subspace of $X$ is isomorphic to a complemented subspace of $X$. This contrasts with the classical result of Lindenstrauss and Tzafriri that a Banach space in which every closed subspace is complemented must be isomorphic to a Hilbert space.
DOI : 10.4007/annals.2012.176.3.10

W. B. Johnson 1 ; A. Szankowski 2

1 Department of Mathematics<br/> Texas A&M University<br/> College Station, TX 77843-3368
2 The Hebrew University of Jerusalem<br/>Jerusalem 91904<br/> Israel 
@article{10_4007_annals_2012_176_3_10,
     author = {W. B. Johnson and A. Szankowski},
     title = {Hereditary approximation property},
     journal = {Annals of mathematics},
     pages = {1987--2001},
     publisher = {mathdoc},
     volume = {176},
     number = {3},
     year = {2012},
     doi = {10.4007/annals.2012.176.3.10},
     mrnumber = {2979863},
     zbl = {06121654},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.10/}
}
TY  - JOUR
AU  - W. B. Johnson
AU  - A. Szankowski
TI  - Hereditary approximation property
JO  - Annals of mathematics
PY  - 2012
SP  - 1987
EP  - 2001
VL  - 176
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.10/
DO  - 10.4007/annals.2012.176.3.10
LA  - en
ID  - 10_4007_annals_2012_176_3_10
ER  - 
%0 Journal Article
%A W. B. Johnson
%A A. Szankowski
%T Hereditary approximation property
%J Annals of mathematics
%D 2012
%P 1987-2001
%V 176
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.10/
%R 10.4007/annals.2012.176.3.10
%G en
%F 10_4007_annals_2012_176_3_10
W. B. Johnson; A. Szankowski. Hereditary approximation property. Annals of mathematics, Tome 176 (2012) no. 3, pp. 1987-2001. doi : 10.4007/annals.2012.176.3.10. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.10/

Cité par Sources :