A new class of Kadison-Singer algebras |
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| Authors: | Liguang Wang Wei Yuan |
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| Institution: | a School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, Chinab Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | We show that the projection lattice generated by a maximal nest and a rank one projection in a separable infinite-dimensional Hilbert space is in general reflexive. Moreover we show that the corresponding reflexive algebra has a maximal triangular property, equivalently, it is a Kadison-Singer algebra. Similar results are also obtained for the lattice generated by a finite nest and a projection in a finite factor. |
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| Keywords: | 46L10 47L75 |
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