In this paper it is shown that the class Ln WU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class Ln WSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.
@article{urn:eudml:doc:39936,
title = {Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.},
journal = {Extracta Mathematicae},
volume = {6},
year = {1991},
pages = {139-141},
mrnumber = {MR1185361},
zbl = {0714.46033},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39936}
}
Asthagiri, Rajappa K. Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.. Extracta Mathematicae, Tome 6 (1991) pp. 139-141. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39936/