On discrete subspaces of a Hilbert space
نویسندگان
چکیده
منابع مشابه
Large and Small Subspaces of Hilbert Space
For example, Theorem 3 says that if V is a closed subspace of f2 and if V CQp for some p < 2, then V is finite-dimensional . On the other hand, the corollary to Theorem 4 states that there exist infinite-dimensional subspaces V of f 2 none of whose nonzero elements belongs to any f p -space (p < 2) . [For L2(0, 1) the results are somewhat different: (1) if V is a closed subspace of L 2(0, 1) an...
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G. BIRKHOFF and J . v . NEUMANN1 have shown in 1936 that the closed linear manifolds (subspaces) of the Hilbert space form a complete atomic and ortho-complemented lattice LQ which at least for finite dimensional subspaces is also modular. JAUCH 2 ' 3 , PIRON4 and KAMBER5 have pointed out, that instead of the modularity a weeker condition can be formulated in LQ which is always fulfilled for th...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1977
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-38-1-53-64