Abstract
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 Frechet algebras of power series in k indeterminates. The proof goes via first completely characterizing these algebras; in particular, it is shown that the Beurling-Frechet 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 the case of Frechet algebras of power series in infinitely many indeterminates.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
