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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Continuity of the spectrum and spectral radius


Author: Gerard J. Murphy
Journal: Proc. Amer. Math. Soc. 82 (1981), 619-621
MSC: Primary 46H20; Secondary 47A10, 47A12
MathSciNet review: 614889
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Abstract: Let $ A$ be a Banach algebra containing an element $ x$. Topological conditions on the spectrum of $ x$ are given which are necessary and sufficient to ensure the continuity of the spectrum or spectral radius at $ x$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0614889-2
Article copyright: © Copyright 1981 American Mathematical Society