Measurability properties of spectra

Levi, S.; Slodkowski, Z.

doi:10.1090/S0002-9939-1986-0854024-3

Measurability properties of spectra
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by S. Levi and Z. Slodkowski PDF

Proc. Amer. Math. Soc. 98 (1986), 225-231 Request permission

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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On closed mappings

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