Modular functions on multilattices

Avallone, Anna

doi:10.1023/a:1021715427024

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2005

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“…There have been numerous studies of group-valued measures on Boolean algebras, orthomodular lattices, and their generalizations (Avallone and Hamhalter, 1996;D'Andrea and De Lucia, 1992;De Lucia and Morales, 1998;García Mazarío, 2001;Göbel et al, 1996;Navara et al, 1993;Bhashkara Rao and Shortt, 1991). Additionally, the group-valued measures on an orthomodular structure L are closely linked to the unigroup of L, a key ingredient in David Foulis' recent algebraic approach to non-commutative measure theory (Bennett and Foulis, 1997;Foulis et al, 1998;Foulis, 2000).…”

Section: Introductionmentioning

confidence: 99%

Group-Valued Measures on the Lattice of Closed Subspaces of a Hilbert Space

2005

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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 R 2n generalizing properties of those used in various treatments of the KochenSpecker theorem in R 4 .

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