Group-Valued Measures on the Lattice of Closed Subspaces of a Hilbert Space
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چکیده
We show there are no non-trivial finite Abelian group-valued measures on the lattice of closed subspaces of an infinite-dimensional Hilbert space, and we use this to establish that the unigroup of the lattice of closed subspaces of an infinite-dimensional Hilbert space is divisible. The main technique is a combinatorial construction of a set of vectors in R2n generalizing properties of those used in various treatments of the Kochen– Specker theorem in R4.
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تاریخ انتشار 2005