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 Gs, and prove that in a Polish algebra the set of invertible elements is an FaSand the inverse mapping is a Borel function of the second class
Levi, S., Slodkowski, Z. (1986). Measurability properties of spectra. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 98(2), 225-231 [10.1090/S0002-9939-1986-0854024-3].
Measurability properties of spectra
LEVI, SANDRO;
1986
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 Gs, and prove that in a Polish algebra the set of invertible elements is an FaSand the inverse mapping is a Borel function of the second class
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