Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Remarks on commuting exponentials in Banach algebras, II

Author(s): Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 128 (2000), 3405-3409.
MSC (1991): Primary 46H99
Posted: May 11, 2000
MathSciNet review: 1691002
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Abstract:

Suppose that and are elements of a complex unital Banach algebra such that the spectrum of is $2\pi i$ -congruence-free and . We show that then is the sum of nilpotent elements. If denotes the spectral radius of , then we show that the additional assumption $r(b)<2 \pi$ implies that $\begin{equation*}b (ab-ba)^2 = (ab-ba)^2 b. \end{equation*}$

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