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The Spectral Diameter in Banach Algebras
Proceedings of the American Mathematical Society
Vol. 91, No. 1 (May, 1984), pp. 59-63
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2045269
Page Count: 5
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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 - uau-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.
Proceedings of the American Mathematical Society © 1984 American Mathematical Society