Topologically Invertible Elements and Topological Spectrum

Volume 54 / 2006

Mati Abel, Wiesław Żelazko 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.

Authors

  • Mati AbelInstitute of Pure Mathematics
    University of Tartu
    Liivi 2-614, 50409 Tartu, Estonia
    e-mail
  • Wiesław ŻelazkoInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 137, Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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