The topology of ideals in some triangular AF algebras. (English) Zbl 0874.46035
Summary: A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this space and ideals in the AF algebra. Some connections with nest representations and nest-primitive ideals are also described.
MSC:
46K50 | Nonselfadjoint (sub)algebras in algebras with involution |
47L30 | Abstract operator algebras on Hilbert spaces |
46L05 | General theory of \(C^*\)-algebras |
46M40 | Inductive and projective limits in functional analysis |