Measurability Properties of Spectra
Copyright policy )Measurability Properties of Spectra
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 δ {G_\delta } , and prove that in a Polish algebra the set of invertible elements is an F σ δ {F_{\sigma \delta }} and the inverse mapping is a Borel function of the second class.
Polish algebra, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), inverse mapping, General theory of topological algebras, Borel measurability of the spectrum in topological algebras, Spectrum mapping; Borel measurability of the spectrum in topological algebras; Polish algebra; inverse mapping, spectrum mapping
Polish algebra, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), inverse mapping, General theory of topological algebras, Borel measurability of the spectrum in topological algebras, Spectrum mapping; Borel measurability of the spectrum in topological algebras; Polish algebra; inverse mapping, spectrum mapping
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