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Banach Algebras with A Discrete Structure Space
2003
Mathematical Proceedings of the Royal Irish Academy
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Let A be a semi-simple Banach algebra and C be its closed two-sided ideals. For K 2 C let K a denote its annihilator in A. The mapping K pK a is shown to be an injective map of C into C if and only if it is surjective and if and only if both the structure space of A is discrete and A/K is semi-simple for every K 2 C. If A has these properties so does K and A/K for each K 2 C. Such A is called bidual. Every K 2 C has a dense socle if and only if A is a bidual modular annihilator algebra.
doi:10.3318/pria.2003.103.2.149
fatcat:3fwo7wtc65et7of2g546xjl4im