The Ideal Structure of Toeplitz Algebras

摘要

We investigate the ideal structure of the Toeplitz algebra T(Γ) of a totally ordered abelian group Γ. We show that the primitive ideals of T(Γ) are parametrised by the disjoint union X of the duals I of the order ideals I of Γ, and identify the hull-kernel topology on when the chain of orderideals in Γ is isomorphic to a subset of {-∞}∪Z∪{∞}.