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Abstract

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].