Geodesic
Fréchet algebras, formal power series, and automatic continuity
S. R. Patel 1
1 Department of Mathematics and Statistics Indian Institute of Technology Kanpur 208 016, Uttar Pradesh, India
Studia Mathematica, Tome 187 (2008) no. 2, pp. 125-136 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm187-2-2
Keywords: describe those commutative chet algebras which may continuously embedded algebra mathbb contain polynomials shown these algebras except mathbb itself always satisfy certain equicontinuity condition due loy using result applications theory automatic continuity given particular uniqueness chet algebra topology algebras established

S. R. Patel  1

1 Department of Mathematics and Statistics Indian Institute of Technology Kanpur 208 016, Uttar Pradesh, India 
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S. R. Patel. Fréchet algebras, formal power series, and automatic continuity. Studia Mathematica, Tome 187 (2008) no. 2, pp. 125-136. doi: 10.4064/sm187-2-2

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