We study measurability of the spectrum in topological algebras. We give some equivalences, prove that the spectrum in a Banach algebra is continuous on a dense Gδ and that in a polish algebra the set of invertible elements is an Fσδ and the inverse mapping a Borel function of the second class
Levi, S. (1986). Measurability properties of the spectrum. RENDICONTI DEL SEMINARIO MATEMATICO E FISICO DI MILANO, 56(1), 85-88 [10.1007/BF02925137].
Measurability properties of the spectrum
Levi, S
1986
Abstract
We study measurability of the spectrum in topological algebras. We give some equivalences, prove that the spectrum in a Banach algebra is continuous on a dense Gδ and that in a polish algebra the set of invertible elements is an Fσδ and the inverse mapping a Borel function of the second class
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