Group-valued measures on the lattice of closed subspaces of a Hilbert space

被引：7
|
作者：
Harding, J [1 ]
Jager, E
Smith, D
机构：
[1] New Mexico State Univ, Dept Math Sci, Las Cruces, NM 88003 USA
[2] Lafayette Coll, Dept Math, Easton, PA 18042 USA
来源：
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2005年 / 44卷 / 05期
关键词：
group-valued measure; Hilbert space; Kochen-Specker theorem; unigroup;
D O I：
10.1007/s10773-005-3981-x
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We show there are no non-trivial finite Abelian group-valued measures on the lattice of closed subspaces of an infinite-imensional 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 Kochen Specker theorem in R-4.
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页码：539 / 548
页数：10
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