Topologies on the space of ideals of a Banach algebra

• Autorzy: Ferdinand Beckhoff
• Języki publikacji: EN

Abstrakty

EN

Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely $τ_∞$, coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra $τ_∞$ coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if $τ_∞$ is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A) with the relative hull kernel topology turn out to be separable Lindelöf spaces if A is separable, which improves results from [14].

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 46H10: Ideals and subalgebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 115
• Numer: 2
• Strony: 189-205

Daty

wydano

1995

otrzymano

1994-12-28

poprawiono

1995-03-02

Twórcy

autor

Ferdinand Beckhoff

• Mathematisches Institut der Universität Münster, Einsteinstr. 62, 48149 Münster, Fed. Rep. Germany

Bibliografia

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