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spectral radius — 1 results found.

      
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Commutativity Criteria in Banach Algebras
C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (3) 2015, pp. 89-93
Cheikh O. Hamoud (Received: 2014/05/30, Revised: 2014/11/10)

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We consider complex Banach algebras satisfying the condition \(\displaystyle (xy)^k=x^ky^k\) for all \(x\,,\,y\,\) in the algebra where \(k\) is an integer \((k\geq 2)\).

We show that for \(k=2\) and \(k=3\), this condition yields commutativity in unital Banach algebras. For higher values of \(k\), commutativity is obtained for semi-simple algebras and the conclusions are quite similar to the ones in Cheikh 1995.

The extension of the results to wider classes of algebras is also considered.

Nous considérons des algèbres de Banach complexes vérifiant la condition \(\displaystyle (xy)^k=x^ky^k\) pour tout \(x\,,\,y\,\) dans l’algèbre, \(k\) étant un entier \((k\geq 2)\).

Nous montrons que pour \(k=2\) et \(k=3\), cette condition entraine la commutativité dans les algèbres de Banach unitaires. Pour les valeurs plus elevées de \(k\), la commutativité est établie dans les algèbres semi-simples avec des résultats similaires à ceux obtenus dans Cheikh 1995.

L’extension des résultats à d’autres classes d’algèbres topologiques est également considérée.

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