The kh-socle of a commutative semisimple Banach algebra

Mathematica Bohemica

关键词: commutative banach algebra;   

DOI  :  10.21136/MB.2019.0106-18

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown