Inequalities pp 147-149 | Cite as

Positive Linear Maps which are Order Bounded on C* Subalgebras

  • Michael Aizenman
  • E. Brian Davies
  • Elliott H. Lieb


When studying the third law of thermodynamics for an infinite system, or properties of equilibrium states of such a system (see [3]), one is led to consider the effect of local perturbations.


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    F. M. Alfsen, “Compact Convex Sets and Boundary Condition,” Springer, Berlin, 1971.CrossRefGoogle Scholar
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    E. B. Davies, “Quantum Theory of Open Systems,” Academic Press, New York, 1976.zbMATHGoogle Scholar
  3. 3.
    G. L. Sewell, KMS conditions and local thermodynamical stability of quantum lattice systems, II, Comm. Math. Phys. 55 (1977), 53.MathSciNetCrossRefGoogle Scholar
  4. 4.
    W. Wils, The ideal center for partially ordered vector spaces, Acta Math. 127 (1971), 41.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    T. B. Andersen, On multipliers and order-bounded operators in C*-algebras, Proc. Amer. Math. Soc. 25 (1970), 896–899MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael Aizenman
    • 1
  • E. Brian Davies
    • 2
  • Elliott H. Lieb
    • 3
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathermaticsPrinceton UniversityPrincetonUSA
  3. 3.Department of Mathematic and PhysicsPrinceton UniversityPrincetonUSA

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