We describe all those commutative Fréchet algebras which may be continuously embedded in the algebra ℂ[[X]] in such a way that they contain the polynomials. It is shown that these algebras (except ℂ[[X]] itself) always satisfy a certain equicontinuity condition due to Loy. Using this result, some applications to the theory of automatic continuity are given; in particular, the uniqueness of the Fréchet algebra topology for such algebras is established.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-2,
author = {S. R. Patel},
title = {Fr\'echet algebras, formal power series, and automatic continuity},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {125-136},
zbl = {1157.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-2}
}
S. R. Patel. Fréchet algebras, formal power series, and automatic continuity. Studia Mathematica, Tome 187 (2008) pp. 125-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-2-2/