Topologically Invertible Elements and Topological Spectrum
Volume 54 / 2006
Bulletin Polish Acad. Sci. Math. 54 (2006), 257-271
MSC: Primary 46H05; Secondary 46H20.
DOI: 10.4064/ba54-3-7
Abstract
Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x\mapsto x^{-1}$ 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.
