On optimal observability of linear systems with infinite-dimensional states

S. Rolewicz

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Topologies on the space of ideals of a Banach algebra

Ferdinand Beckhoff (1995)

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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 $τ_{\infty}$ , coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra $τ_{\infty}$ 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 $τ_{\infty}$ is Hausdorff; this generalizes results from [1] and [5]. All subspaces...