Geodesic
Uniqueness of the Fréchet algebra topology on certain Fréchet algebras
S. R. Patel1
1 Department of Mathematics C. U. Shah University Wadhwan City, Gujarat, India
Studia Mathematica, Tome 234 (2016) no. 1, pp. 31-47

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In 1978, Dales posed a question about the uniqueness of the $(F)$-algebra topology for $(F)$-algebras of power series in $k$ indeterminates. We settle this in the affirmative for Fréchet algebras of power series in $k$ indeterminates. The proof goes via first completely characterizing these algebras; in particular, it is shown that the Beurling–Fréchet algebras of semiweight type do not satisfy a certain equicontinuity condition due to Loy. Some applications to the theory of automatic continuity are also given, in particular to the case of Fréchet algebras of power series in infinitely many indeterminates.
DOI : 10.4064/sm8132-5-2016
Mots-clés : dales posed question about uniqueness algebra topology algebras power series indeterminates settle affirmative chet algebras power series indeterminates proof goes via first completely characterizing these algebras particular shown beurling chet algebras semiweight type satisfy certain equicontinuity condition due loy applications theory automatic continuity given particular chet algebras power series infinitely many indeterminates

S. R. Patel 1

1 Department of Mathematics C. U. Shah University Wadhwan City, Gujarat, India 
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S. R. Patel. Uniqueness of the Fréchet algebra topology on certain Fréchet algebras. Studia Mathematica, Tome 234 (2016) no. 1, pp. 31-47. doi: 10.4064/sm8132-5-2016

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