On the ideal structure of Banach algebras

Dietrich, William E.

doi:10.1090/S0002-9947-1972-0308791-2

On the ideal structure of Banach algebras
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Trans. Amer. Math. Soc. 169 (1972), 59-74 Request permission

Abstract:

For Banach algebras $A$ in a class which includes all group and function algebras, we show that the family of ideals of $A$ with the same hull is typically quite large, containing ascending and descending chains of arbitrary length through any ideal in the family, and that typically a closed ideal of $A$ whose hull meets the Šilov boundary of $A$ cannot be countably generated algebraically.

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