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  3. Operator Algebras in Dynamical Systems
  • Cited by 92
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2010
      August 1991
      ISBN:
      9780511662218
      9780521400961
      9780521060219
      DOI:
      https://doi.org/10.1017/CBO9780511662218
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.524kg, 232 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.339kg, 232 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (41)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (41)
    Information

    Book description

    This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.

    Reviews

    "The theory for the normal derivations is developed very clearly in this important book, and the subject is one of the most central ones in the modern theory of operator algebras. It is written by one of the prime movers, and it is addressed to a wide audience. It should be a useful introduction to the subject." Palle E.T. Jørgensen, Mathematical Reviews

    "...makes for pleasant browsing and really worthwhile reading....This volume is a gem!" Richard V. Kadison, Bulletin of the American Mathematical Society

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