Geodesic
A NOTE ON CONTINUOUS RESTRICTIONS OF LINEAR MAPS BETWEEN BANACH SPACES
Acta mathematica Universitatis Comenianae, Tome 61 (1992) no. 2 
M. I. Ostrovskii. A NOTE ON CONTINUOUS RESTRICTIONS OF LINEAR MAPS BETWEEN BANACH SPACES. Acta mathematica Universitatis Comenianae, Tome 61 (1992) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a3/
@article{AMUC_1992_61_2_a3,
     author = {M. I. Ostrovskii},
     title = {A {NOTE} {ON} {CONTINUOUS} {RESTRICTIONS} {OF} {LINEAR} {MAPS} {BETWEEN} {BANACH} {SPACES}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1992},
     volume = {61},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a3/}
}
TY  - JOUR
AU  - M. I. Ostrovskii
TI  - A NOTE ON CONTINUOUS RESTRICTIONS OF LINEAR MAPS BETWEEN BANACH SPACES
JO  - Acta mathematica Universitatis Comenianae
PY  - 1992
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a3/
ID  - AMUC_1992_61_2_a3
ER  - 
%0 Journal Article
%A M. I. Ostrovskii
%T A NOTE ON CONTINUOUS RESTRICTIONS OF LINEAR MAPS BETWEEN BANACH SPACES
%J Acta mathematica Universitatis Comenianae
%D 1992
%V 61
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_1992_61_2_a3/
%F AMUC_1992_61_2_a3

Voir la notice de l'article provenant de la source Comenius University

This note is devoted to the answers to the following questions asked by V. I. Bogachev, B. Kirchheim and W. Schachermayer:\newline 1. Let $T\: l_1\to X$ be a linear map into the infinite dimensional Banach space $X$. Can one find a closed infinite dimensional subspace $Z\subset l_1$ such that $T\big|_\ZZ$ is continuous?\newline 2. Let $X=c_0$ or $X=l_p$ ($1) and let $T\: X\to X$ be a linear map. Can one find a dense subspace $Z$ of $X$ such that \tz is continuous?