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

J. A. Brooke·P. Busch·D. B. Pearson
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Abstract

We explore commutativity up to a factor, $AB=λBA$, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor $λ$ 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 nontrivial realizations of such commutation relations are given.

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J. A. Brooke, P. Busch, D. B. Pearson. 2001-05-25. Commutativity up to a factor of bounded operators in complex Hilbert space. https://doi.org/10.1098/rspa.2001.0858

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