The spectral diameter in Banach algebras

Grabiner, Sandy

doi:10.1090/S0002-9939-1984-0735564-2

The spectral diameter in Banach algebras
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Proc. Amer. Math. Soc. 91 (1984), 59-63 Request permission

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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