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Commutativity up to a factor of bounded operators in complex Hilbert space | | J.A. Brooke
; P. Busch
; D.B. Pearson
; | | Date: |
9 Jul 2000 | | Journal: | Proc. Roy. Soc. A (London) 458 (2002) 109-118. | | Subject: | Functional Analysis; Mathematical Physics MSC-class: 46N50; 47A05; 81P15 | math.FA math-ph math.MP quant-ph | | 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. | | Source: | arXiv, math.FA/0007049 | | Services: | Forum | Review | PDF | Favorites | |
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