Topologically Invertible Elements and Topological Spectrum

• Autorzy: Mati Abel , Wiesław Żelazko
• Języki publikacji: EN

Abstrakty

EN

Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x ↦ x^{-1}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.

Kategorie tematyczne

• 46H20: Structure, classification of topological algebras
• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: 54
• Numer: 3
• Strony: 257-271

Daty

wydano

2006

Twórcy

autor

Mati Abel

• Institute of Pure Mathematics, University of Tartu, Liivi 2-614, 50409 Tartu, Estonia

autor

Wiesław Żelazko

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba54-3-7