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Keywords:
commutative Banach algebra; socle; kh-socle; inessential element
commutative Banach algebra; socle; kh-socle; inessential element
Summary:
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.
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