Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.
@article{urn:eudml:doc:41146,
title = {Discontinuity of the product in multiplier algebras.},
journal = {Publicacions Matem\`atiques},
volume = {34},
year = {1990},
pages = {397-401},
zbl = {0726.46029},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41146}
}
Oudadess, Mohamed. Discontinuity of the product in multiplier algebras.. Publicacions Matemàtiques, Tome 34 (1990) pp. 397-401. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41146/