Gibbs Semigroups

  • Valentin A. Zagrebnov

Part of the Operator Theory: Advances and Applications book series (OT, volume 273)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Valentin A. Zagrebnov
    Pages 1-40
  3. Valentin A. Zagrebnov
    Pages 41-79
  4. Valentin A. Zagrebnov
    Pages 81-98
  5. Valentin A. Zagrebnov
    Pages 99-142
  6. Valentin A. Zagrebnov
    Pages 143-208
  7. Valentin A. Zagrebnov
    Pages 209-243
  8. Valentin A. Zagrebnov
    Pages 245-256
  9. Back Matter
    Pages 257-319

About this book


This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development.  It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal.

By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics.


operator semigroups and generators trace ideals Gibbs semigroups Lie-Trotter-Kato product formulae Symmetrically-normed ideals Dixmier ideal and trace

Authors and affiliations

  • Valentin A. Zagrebnov
    • 1
  1. 1.Université d’Aix-MarseilleInstitut de Mathématiques de MarseilleMarseilleFrance

Bibliographic information