J. A. Brooke, P. Busch, D. B. Pearson
Published 2000-07-09, updated 2001-05-25Version 3
We explore commutativity up to a factor, $AB=\lambda BA$, 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 nontrivial realizations of such commutation relations are given.
Comments: 9 pages. Material reorganised, new examples added to highlight relations between main results. Submitted to Proc. Roy. Soc. A
Journal: Proc. Roy. Soc. A (London) 458 (2002) 109-118.
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