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

J.A. Brooke; Paul Busch; D.B. Pearson

doi:10.1098/rspa.2001.0858

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

J.A. Brooke, Paul Busch, D.B. Pearson

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We explore commutativity up to a factor, AB = uBA, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor u 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.

Original language	English
Pages (from-to)	109-118
Number of pages	9
Journal	Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Volume	458
Issue number	2017
DOIs	https://doi.org/10.1098/rspa.2001.0858
Publication status	Published - Jan 2002

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10.1098/rspa.2001.0858

http://dx.doi.org/10.1098/rspa.2001.0858

Cite this

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abstract = "We explore commutativity up to a factor, AB = uBA, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor u 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.",

author = "J.A. Brooke and Paul Busch and D.B. Pearson",

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