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<p>Firstly, it is proved that the distributive KS-lattice on a Hilbert space contains no non-trivial reducing projections. Secondly, the necessary and sufficient conditions are given for the projection lattice generated by one-point extensions of finite-nests on a Hilbert space to be a KS-lattice. Finally, all derivations on the projection lattice algebra corresponding to the projection lattice generated by one-point extensions of nests are characterized as inner derivations.</p>

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Structure and construction of Kadison–Singer lattices

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Jun He,
  • Xinyu Liu,
  • Guangyu An

摘要

Firstly, it is proved that the distributive KS-lattice on a Hilbert space contains no non-trivial reducing projections. Secondly, the necessary and sufficient conditions are given for the projection lattice generated by one-point extensions of finite-nests on a Hilbert space to be a KS-lattice. Finally, all derivations on the projection lattice algebra corresponding to the projection lattice generated by one-point extensions of nests are characterized as inner derivations.