Geodesic
The kh-socle of a commutative semisimple Banach algebra
Mathematica Bohemica, Tome 145 (2020) no. 4, pp. 387-399.

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Let $\mathcal {A}$ be a commutative complex semisimple Banach algebra. Denote by ${\rm kh}({\rm soc}(\mathcal {A}))$ the kernel of the hull of the socle of $\mathcal {A}$. In this work we give some new characterizations of this ideal in terms of minimal idempotents in $\mathcal {A}$. This allows us to show that a ``result'' from Riesz theory in commutative Banach algebras is not true.
DOI : 10.21136/MB.2019.0106-18
Classification : 46J05, 46J20, 47A10
Keywords: commutative Banach algebra; socle; kh-socle; inessential element 
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Hadder, Youness. The kh-socle of a commutative semisimple Banach algebra. Mathematica Bohemica, Tome 145 (2020) no. 4, pp. 387-399. doi : 10.21136/MB.2019.0106-18. http://geodesic.mathdoc.fr/articles/10.21136/MB.2019.0106-18/

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