2015 | OriginalPaper | Buchkapitel
Minimal Primal Ideals in the Multiplier Algebra of a C 0(X)-algebra
verfasst von : R. J. Archbold, D. W. B. Somerset
Erschienen in: Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
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Let A be a stable, σ-unital, continuous C0(X)-algebra with surjective base map φ : $$\mathrm{Prim}(A)\;\rightarrow X$$ , where Prim(A) is the primitive ideal space of the C*-algebra A. Suppose that $$\phi^{-1}(x)$$ is contained in a limit set in Prim(A) for each $$x \in X$$ (so that A is quasi-standard). Let CR(X) be the ring of continuous real-valued functions on X. It is shown that there is a homeomorphism between the space of minimal prime ideals of CR(X) and the space MinPrimal(M(A)) of minimal closed primal ideals of the multiplier algebra M(A). If A is separable then MinPrimal(M(A)) is compact and extremally disconnected but if $$X = \beta \bf{N} \setminus \bf{N}$$ then MinPrimal(M(A)) is nowhere locally compact.