Abstract
We show that an advertibly complete A-p normed algebra E is isomorphic to the complex field C, modulo its radical, in any of the following cases: 1) every element of E has a star-shaped spectrum, 2) E is involutive and every normal element of E has a star-shaped spectrum; 3) E is hermitian and every unitary element of E has a star-shaped spectrum.
Publisher
Universidad Nacional de Colombia
Reference9 articles.
1. B. Aupetit, A primer on spectral theory, Universitext. Springer-Verlag, New York, 1991.
2. S. Bhatt, Spectrally convex Banach algebras, Indian J. Pure Appl. Math. 10 (1979), no. 6, 726-730.
3. F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, New York-Heidelberg, 1973.
4. I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418.
5. A. Ouhmidou and A. El Kinani, On Spectrally convex ordinary algebras, Indian J. Pure Appl. Math. 53 (2022), no. 2, 349-354.