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Fréchet algebras, formal power series, and automatic continuity

Tom 187 / 2008

Studia Mathematica 187 (2008), 125-136 MSC: Primary 46J05; Secondary 13F25, 46H40. DOI: 10.4064/sm187-2-2

Streszczenie

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.

Autorzy

• S. R. PatelDepartment of Mathematics and Statistics
Indian Institute of Technology
Kanpur 208 016, Uttar Pradesh, India
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