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

J. A. Brooke; P. Busch; D. B. Pearson

doi:10.1098/rspa.2001.0858

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

Functional Analysis 2009-10-31 v3 Mathematical Physics math.MP Quantum Physics

Authors: J. A. Brooke , P. Busch , D. B. Pearson

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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.

Keywords

operator theory on hilbert spaces operator theory calderon-zygmund operator

Cite

@article{arxiv.math/0007049,
  title  = {Commutativity up to a factor of bounded operators in complex Hilbert space},
  author = {J. A. Brooke and P. Busch and D. B. Pearson},
  journal= {arXiv preprint arXiv:math/0007049},
  year   = {2009}
}

Comments

9 pages. Material reorganised, new examples added to highlight relations between main results. Submitted to Proc. Roy. Soc. A

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

Abstract

Keywords

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