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Commutativity via spectra of exponentials
Published online by Cambridge University Press: 02 November 2021
Abstract
Let A be a semisimple, unital, and complex Banach algebra. It is well known and easy to prove that A is commutative if and only
$e^xe^y=e^{x+y}$
for all
$x,y\in A$
. Elaborating on the spectral theory of commutativity developed by Aupetit, Zemánek, and Zemánek and Pták, we derive, in this paper, commutativity results via a spectral comparison of
$e^xe^y$
and
$e^{x+y}$
.
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- © Canadian Mathematical Society, 2021
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