Geodesic
Topologically Invertible Elements and Topological Spectrum
Mati Abel 1   ; Wiesław Żelazko 2
1 Institute of Pure Mathematics University of Tartu Liivi 2-614, 50409 Tartu, Estonia
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 137, Śniadeckich 8 00-956 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 3, pp. 257-271 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba54-3-7
Keywords: properties topologically invertible elements topological spectrum elements unital semitopological algebras studied shown inversion mapsto continuous every invertive chet algebra singly generated unital semitopological algebras have continuous characters only topological spectrum generator non empty several problems presented

Mati Abel  1   ; Wiesław Żelazko  2

1 Institute of Pure Mathematics University of Tartu Liivi 2-614, 50409 Tartu, Estonia
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 137, Śniadeckich 8 00-956 Warszawa, Poland 
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     title = {Topologically {Invertible} {Elements} and {Topological} {Spectrum}},
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Mati Abel; Wiesław Żelazko. Topologically Invertible Elements and Topological Spectrum. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 3, pp. 257-271. doi: 10.4064/ba54-3-7

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