Geodesic
Commutativity via spectra of exponentials
Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 815-824

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DOI

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 $e^{x+y}$.
DOI : 10.4153/S0008439521000886
Mots-clés : Spectrum, exponential function, Banach algebra, commutativity 
Brits, Rudi; Schulz, Francois; Touré, Cheick. Commutativity via spectra of exponentials. Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 815-824. doi: 10.4153/S0008439521000886
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     title = {Commutativity via spectra of exponentials},
     journal = {Canadian mathematical bulletin},
     pages = {815--824},
     year = {2022},
     volume = {65},
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     doi = {10.4153/S0008439521000886},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000886/}
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