Geodesic
A multiplicative Kowalski–Słodkowski theorem for $C^\star $-algebras
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 951-958

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DOI

We present here a multiplicative version of the classical Kowalski–Słodkowski theorem, which identifies the characters among the collection of all functionals on a complex and unital Banach algebra A. In particular, we show that, if A is a $C^\star $-algebra, and if $\phi :A\to \mathbb C $ is a continuous function satisfying $ \phi (x)\phi (y) \in \sigma (xy) $ for all $x,y\in A$ (where $\sigma $ denotes the spectrum), then either $\phi $ is a character of A or $-\phi $ is a character of A.
DOI : 10.4153/S0008439522000662
Mots-clés : C*-algebra, linear functional, multiplicative functional, character, Kowalski–Słodkowski theorem, Gleason–Kahane–Żelazko theorem 
Touré, Cheick; Brits, Rudi; Sebastian, Geethika. A multiplicative Kowalski–Słodkowski theorem for $C^\star $-algebras. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 951-958. doi: 10.4153/S0008439522000662
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     author = {Tour\'e, Cheick and Brits, Rudi and Sebastian, Geethika},
     title = {A multiplicative {Kowalski{\textendash}S{\l}odkowski} theorem for $C^\star $-algebras},
     journal = {Canadian mathematical bulletin},
     pages = {951--958},
     year = {2023},
     volume = {66},
     number = {3},
     doi = {10.4153/S0008439522000662},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000662/}
}
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