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Remarks on commuting exponentials in Banach algebras, II


Author: Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 128 (2000), 3405-3409
MSC (1991): Primary 46H99
DOI: https://doi.org/10.1090/S0002-9939-00-05465-4
Published electronically: May 11, 2000
MathSciNet review: 1691002
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Abstract:

Suppose that $a$ and $b$ are elements of a complex unital Banach algebra such that the spectrum of $a$ is $2\pi i$-congruence-free and $e^ae^b = e^be^a$. We show that then $ab-ba$ is the sum of nilpotent elements. If $r(b)$ denotes the spectral radius of $b$, 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*}


References [Enhancements On Off] (What's this?)

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Additional Information

Christoph Schmoeger
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: christoph.schmoeger@math.uni-karlsruhe.de

DOI: https://doi.org/10.1090/S0002-9939-00-05465-4
Keywords: Commuting exponentials
Received by editor(s): August 28, 1998
Received by editor(s) in revised form: January 22, 1999
Published electronically: May 11, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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