Commutativity up to a factor of bounded operators in complex Hilbert space

被引：38

作者：

Brooke, JA ^{[1
]}

Busch, P

Pearson, DB

机构：

[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK S7N 5E6, Canada

[2] Univ Hull, Dept Math, Kingston Upon Hull HU6 7RX, N Humberside, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2002年 / 458卷 / 2017期

关键词：

Hilbert space operators; commutator; commutation relations; self-adjointness; positivity; quantum measurement theory;

D O I：

10.1098/rspa.2001.0858

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We explore commutativity up to a factor, AB = lambdaBA, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor lambda are formulated and shown to depend on spectral properties of the operators involved. Commutativity up to a unitary factor is considered for pairs of self-adjoint operators. Examples of non-trivial realizations of such commutation relations are given.

引用

页码：109 / 118

页数：10

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