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 | References | Similar Articles | Additional Information
Abstract: The element is in the center of the Banach algebra
modulo its radical if and only if there is an upper bound for the diameters of the spectra of
for
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