Fréchet algebras, formal power series, and automatic continuity
Volume 187 / 2008
Studia Mathematica 187 (2008), 125-136
MSC: Primary 46J05;
Secondary 13F25, 46H40.
DOI: 10.4064/sm187-2-2
Abstract
We describe all those commutative Fréchet algebras which may be continuously embedded in the algebra $\mathbb{C}[[X]]$ in such a way that they contain the polynomials. It is shown that these algebras (except $\mathbb{C}[[X]]$ 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.
