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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Measurability properties of spectra


Authors: S. Levi and Z. Slodkowski
Journal: Proc. Amer. Math. Soc. 98 (1986), 225-231
MSC: Primary 46H05; Secondary 54H05
DOI: https://doi.org/10.1090/S0002-9939-1986-0854024-3
MathSciNet review: 854024
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Abstract: We study Borel measurability of the spectrum in topological algebras. We give some equivalences of the various properties, show that the spectrum in a Banach algebra is continuous on a dense $ {G_\delta }$, and prove that in a Polish algebra the set of invertible elements is an $ {F_{\sigma \delta }}$ and the inverse mapping is a Borel function of the second class.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0854024-3
Article copyright: © Copyright 1986 American Mathematical Society