Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind En be a separated inductive limit of the locally convex spaces. Then ind L(En) is a topological subspace of L(E).
@article{urn:eudml:doc:41102, title = {Inductive limits of vector-valued sequence spaces.}, journal = {Publicacions Matem\`atiques}, volume = {33}, year = {1989}, pages = {363-367}, zbl = {0728.46006}, mrnumber = {MR1030973}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41102} }
Bonet, José; Dierolf, Susanne; Fernández, Carmen. Inductive limits of vector-valued sequence spaces.. Publicacions Matemàtiques, Tome 33 (1989) pp. 363-367. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41102/