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La deuxième conjecture de Hirschfeld-Żelazko pour les algèbres de Banach est fausse


Author: Bernard Aupetit
Journal: Proc. Amer. Math. Soc. 70 (1978), 161-162
MSC: Primary 46H20
DOI: https://doi.org/10.1090/S0002-9939-1978-0473828-8
MathSciNet review: 0473828
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Abstract: We prove that there exists a noncommutative complex Banach algebra with no quasi-nilpotents elements such that the spectrum function is continuous for the Hausdorff metric.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0473828-8
Keywords: Commutative Banach algebra, quasi-nilpotent elements, spectrum, spectral radius, continuity of the spectrum, irreducible representations
Article copyright: © Copyright 1978 American Mathematical Society