Abstract
Let \(\mathcal{N}\) be a maximal and discrete nest on a separable Hilbert space \(\mathcal{H},E_\xi\) the projection from \(\mathcal{H}\) onto the subspace [ℂξ] spanned by a particular separating vector ξ for \(\mathcal{N}'\) and Q the projection from \(\mathcal{K} = \mathcal{H} \oplus \mathcal{H}\) onto the closed subspace \(\left\{ {\left( {\eta ,\eta } \right):\eta \in \mathcal{H}} \right\}\). Let \(\mathcal{L}\) be the closed lattice in the strong operator topology generated by the projections and Q. We show that \(\mathcal{L}\) is a Kadison-Singer lattice with trivial commutant, i.e., \(\mathcal{L}' = \mathbb{C}I\). Furthermore, we similarly construct some Kadison-Singer lattices in the matrix algebras M 2n (ℂ) and M 2n−1(ℂ).
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Ren, Y., Wu, W. Some new classes of Kadison-Singer lattices in Hilbert spaces. Sci. China Math. 57, 837–846 (2014). https://doi.org/10.1007/s11425-013-4766-y
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DOI: https://doi.org/10.1007/s11425-013-4766-y