Fréchet algebras, formal power series, and automatic continuity

• Autorzy: S. R. Patel
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13F25: Formal power series rings
• 46H40: Automatic continuity
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 2
• Strony: 125-136

Daty

wydano

2008

Twórcy

autor

S. R. Patel

• Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208 016, Uttar Pradesh, India

Identyfikatory

DOI

10.4064/sm187-2-2