Geodesic
$w^*$-basic sequences and reflexivity of Banach spaces
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 677-681

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $\mathcal L(X,Y)$ is not reflexive for reflexive $X$ and $Y$ then $\mathcal L(X_1, Y)$ is is not reflexive for some $X_1\subset X$, $X_1$ having a basis.
Classification : 46B10, 46B15, 46B28
Keywords: reflexive Banach space; Schauder basis; quotient space; w$^*$-basic sequence; tensor product 
@article{CMJ_2005__55_3_a8,
     author = {John, Kamil},
     title = {$w^*$-basic sequences and reflexivity of {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {677--681},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2005},
     mrnumber = {2153091},
     zbl = {1081.46017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a8/}
}
TY  - JOUR
AU  - John, Kamil
TI  - $w^*$-basic sequences and reflexivity of Banach spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 677
EP  - 681
VL  - 55
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a8/
LA  - en
ID  - CMJ_2005__55_3_a8
ER  - 
%0 Journal Article
%A John, Kamil
%T $w^*$-basic sequences and reflexivity of Banach spaces
%J Czechoslovak Mathematical Journal
%D 2005
%P 677-681
%V 55
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a8/
%G en
%F CMJ_2005__55_3_a8
John, Kamil. $w^*$-basic sequences and reflexivity of Banach spaces. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 677-681. http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a8/