Commutativity up to a factor of bounded operators in complex Hilbert space
Abstract
We explore commutativity up to a factor, AB=λ BA, 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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