Certain Distributive Lattices of Subspaces are Reflexive

Certain Distributive Lattices of Subspaces are Reflexive
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DOI:
10.1112/jlms/s2-8.1.51
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发表时间:
1974-05
影响因子:
1.2
通讯作者:
K. Harrison
K. Harrison
中科院分区:
数学2区
文献类型:
--
作者:
K. Harrison

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For each set 5£ of subspaces of a Hilbert space H, let Alg J § ? denote the set of all operators on H, which leave invariant each subspace in if, and for each set s4 of operators on H, let Lat s# denote the set of all subspaces of H which are invariant under each operator in stf.(Note: in this context Hilbert spaces are real or complex, complete, inner-product spaces, subspaces are closed linear manifolds, and operators are bounded linear transformations.)