Isomorphisms of certain CSL algebras
Isomorphisms of certain CSL algebras
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DOI：
10.1016/0022-1236(86)90039-x
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发表时间：
1986-06
影响因子：
1.7
通讯作者：
F. Gilfeather;R. Moore
中科院分区：
文献类型：
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作者：
F. Gilfeather;R. Moore
证明了Hilbert空间上具有交换子空间格(CSL)的两个自反算子代数之间的同构是自动连续的，并导出了格之间的同构.对于具有完全分配子空间格的这类代数，CDC代数的“准空间”实现同构恰好是那些保持所有有限秩算子序的同构。我们给出了一些非空间同构的例子，并讨论了格上确保所有同构都是空间实现的一些充分条件。研究了CSL代数的同构与导子之间的关系。
We show that an isomorphism between two reflexive operator algebras on Hilbert space with commutative subspace lattices (CSL) is automatically continuous and induces an isomorphism between the lattices. For such algebras with completely distributive subspace lattices, CDC algebras, the “quasi-spatially” implemented isomorphisms are shown to be exactly those that preserve the rank of all finite-rank operators. We present some examples of nonspatial isomorphisms and discuss some sufficient conditions on the lattices that ensure that all isomorphisms be spatially implemented. The relationship between isomorphisms and derivations of CSL algebras is also investigated.