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.

引用

页码：539 / 548

页数：10

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