Communications in Mathematical Physics

, Volume 136, Issue 3, pp 625–632 | Cite as

Continuity and relative hamiltonians

  • Matthew J. Donald


Let (ω n ) n ≧1 be a norm convergent sequence of normal states on a von Neumann algebraA withω n ω. Let (k n ) n≧1 be a strongly convergent sequence of self-adjoint elements ofA withk n k. It is shown that the sequence\((\omega _n^{k_n } )_{n \geqq 1} \) of perturbed states converges in norm toω ω . A related result holds forC*-algebras. A counter-example is provided to show that it is not sufficient to assume weak convergence of (ω n ) n ≧1 even whenkn=k for alln. However, conditions are given which, together with weak convergence, are sufficient. Relative entropy methods are used, and a relative entropy inequality is proved.


Entropy Neural Network Statistical Physic Normal State Complex System 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Matthew J. Donald
    • 1
  1. 1.The Cavendish LaboratoryCambridgeUK

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