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The spectral diameter in Banach algebras


Author: Sandy Grabiner
Journal: Proc. Amer. Math. Soc. 91 (1984), 59-63
MSC: Primary 46H05; Secondary 47A65
DOI: https://doi.org/10.1090/S0002-9939-1984-0735564-2
MathSciNet review: 735564
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Abstract: The element $ a$ is in the center of the Banach algebra $ A$ modulo its radical if and only if there is an upper bound for the diameters of the spectra of $ {a^\_}ua{u^{ - 1}}$ for $ u$ invertible. Applications of this result are given to general Banach algebras and to the essential spectrum of operators on a Hilbert Space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0735564-2
Keywords: Spectral diameter, radical, center, commutativity
Article copyright: © Copyright 1984 American Mathematical Society

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