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Nest Representations of TAF Algebras
Published online by Cambridge University Press: 20 November 2018
Abstract
A nest representation of a strongly maximal $\text{TAF}$ algebra
$A$ with diagonal
$D$ is a representation
$\pi $ for which
$\text{Lat}\,\pi \left( A \right)$ 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
$\text{ }\!\!\pi\!\!\text{ }{{\left( D \right)}^{\prime \prime }}$ contains an atom.
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- Research Article
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- Copyright © Canadian Mathematical Society 2000
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