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

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JournalProceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
DatePublished - Jan 2002
Issue number2017
Volume458
Number of pages9
Pages (from-to)109-118
Original languageEnglish

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.

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