Measurability properties of spectra
HTML articles powered by AMS MathViewer
- 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.References
- Bernard Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Mathematics, vol. 735, Springer, Berlin, 1979 (French). MR 549769
- Edward Beckenstein, Lawrence Narici, and Charles Suffel, Topological algebras, North-Holland Mathematics Studies, Vol. 24, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0473835
- S. Banach, Remarques sur les groupes et les corps métriques, Studia Math. 10 (1948), 178–181 (French). MR 29381, DOI 10.4064/sm-10-1-178-181
- V. L. Klee Jr., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc. 3 (1952), 484–487. MR 47250, DOI 10.1090/S0002-9939-1952-0047250-4
- Sandro Levi and Ashok Maitra, Borel measurable images of Polish spaces, Proc. Amer. Math. Soc. 92 (1984), no. 1, 98–102. MR 749900, DOI 10.1090/S0002-9939-1984-0749900-4
- A. L. Shields, The spectrum of an operator of an $F$-space, Proc. Roy. Irish Acad. Sect. A 74 (1974), 291–292. Spectral Theory Symposium (Trinity College, Dublin, 1974). MR 361830
- Zbigniew Słodkowski, Borel sets and the spectrum of an operator on an $F$-space, Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), no. 3-4, 257–261. MR 647605, DOI 10.1017/S0308210500015481 I. A. Vainstein, On closed mappings, Dokl. Akad. Nauk SSSR 57 (1947), 319-323 (Russian).
Additional Information
- © Copyright 1986 American Mathematical Society
- 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