Geodesic
An ordinal version of some applications of the classical interpolation theorem
Fundamenta Mathematicae, Tome 152 (1997) no. 1, pp. 55-74

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

Let E be a Banach space with a separable dual. Zippin's theorem asserts that E embeds in a Banach space $E_1$ with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space $E_2$ with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of $E_1$ and $E_2$ can be controlled by the Szlenk index of E, where the Szlenk index is an ordinal index associated with a separable Banach space which provides a transfinite measure of the separability of the dual space. 
Benoît Bossard. An ordinal version of some applications of the classical interpolation theorem. Fundamenta Mathematicae, Tome 152 (1997) no. 1, pp. 55-74. doi: 10.4064/fm_1997_152_1_1_55_74
@article{10_4064_fm_1997_152_1_1_55_74,
     author = {Beno{\^\i}t Bossard},
     title = {An ordinal version of some applications of the classical interpolation theorem},
     journal = {Fundamenta Mathematicae},
     pages = {55--74},
     year = {1997},
     volume = {152},
     number = {1},
     doi = {10.4064/fm_1997_152_1_1_55_74},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm_1997_152_1_1_55_74/}
}
TY  - JOUR
AU  - Benoît Bossard
TI  - An ordinal version of some applications of the classical interpolation theorem
JO  - Fundamenta Mathematicae
PY  - 1997
SP  - 55
EP  - 74
VL  - 152
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm_1997_152_1_1_55_74/
DO  - 10.4064/fm_1997_152_1_1_55_74
LA  - en
ID  - 10_4064_fm_1997_152_1_1_55_74
ER  - 
%0 Journal Article
%A Benoît Bossard
%T An ordinal version of some applications of the classical interpolation theorem
%J Fundamenta Mathematicae
%D 1997
%P 55-74
%V 152
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm_1997_152_1_1_55_74/
%R 10.4064/fm_1997_152_1_1_55_74
%G en
%F 10_4064_fm_1997_152_1_1_55_74

Cité par Sources :