A nest representation of a strongly maximal TAF algebra $A$ with diagonal $D$ is a representation $\pi$ for which $\lat \pi(A)$ is totally ordered. We prove that $\ker \pi$ is a meet irreducible ideal if the spectrum of $A$ is totally ordered or if (after an appropriate similarity) the von Neumann algebra $\pi(D)''$ contains an atom.

Keywords:

nest representation, meet irreducible ideal, strongly maximal TAF algebra nest representation, meet irreducible ideal, strongly maximal TAF algebra

MSC Classifications:

47L40, 47L35 show english descriptions Limit algebras, subalgebras of $C^*$-algebras
Nest algebras, CSL algebras 47L40 - Limit algebras, subalgebras of $C^*$-algebras
47L35 - Nest algebras, CSL algebras

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