# Commutativity up to a Factor of Bounded Operators in Complex Hilbert Space

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 Title Commutativity up to a Factor of Bounded Operators in Complex Hilbert Space Publication Type Journal Article Year of Publication 2002 Authors Brooke J, Busch P, Pearson D Journal Proc. Roy. Soc. A (Lond.) Volume 458 Pagination 109-118 Abstract 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. URL http://arxiv.org/abs/math.FA/0007049 DOI 10.1098/rspa.2001.0858 E-print number arXiv:math.FA/0007049 MathRev MR1879460