We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.
Probamos que un álgebra localmente convexa con multiplicación continua es automáticamente localmente-m-convexa, si contiene un ideal bilátero I tal que tanto I como el álgebra cociente A/I son localmente-m-convexas. Se presenta una aplicación al comportamiento de la topología localmente-m-convexa asociada en los ideales.
@article{urn:eudml:doc:40971,
title = {The three-space-problem for locally-m-convex algebras.},
journal = {RACSAM},
volume = {97},
year = {2003},
pages = {223-227},
mrnumber = {MR2068175},
zbl = {1076.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40971}
}
Dierolf, Susanne; Heintz, Thomas. The three-space-problem for locally-m-convex algebras.. RACSAM, Tome 97 (2003) pp. 223-227. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40971/