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

Authors:	John?Harding author-information" > author-information__contact u-icon-before" > mailto:jharding@nmsu.edu" title=" jharding@nmsu.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Ekaterina?Jager,Derek?Smith

Affiliation:	(1) Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico;(2) Department of Mathematics, Lafayette College, Easton, Pennsylvania;(3) Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico, 88003

Abstract:	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 R²ⁿgeneralizing properties of those used in various treatments of the Kochen–Specker theorem in R⁴.

Keywords:	group-valued measure Hilbert space Kochen– Specker theorem unigroup
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