Overview
- Provides unique insights on the Gibbs semigroups theory
- Extends the theory to general results
- Includes three appendices
Part of the book series: Operator Theory: Advances and Applications (OT, volume 273)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (7 chapters)
Keywords
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.
Reviews
“This well-written and organized book is a reader-friendly manual in the field of Gibbs semigroups. It can be recommended for experts and graduate, postgraduate, and doctoral students.” (Michael Perelmuter, zbMATH 1512.47004, 2023)
“The book captures a fascinating snapshot of the current state of Gibbs semigroup theory. The book also provides references to the rich literature, nice historical remarks, and inspiring comments on the topics. It is readable and appropriate for readers who are familiar with the basics of functional analysis and linear operator theory. As such, the book will appeal to students at the senior undergraduate and graduate levels as well as researchers in mathematics and mathematical physics.” (Min He, Mathematical Reviews, June, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Gibbs Semigroups
Authors: Valentin A. Zagrebnov
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-030-18877-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-18876-4Published: 27 November 2019
Softcover ISBN: 978-3-030-18879-5Published: 27 November 2020
eBook ISBN: 978-3-030-18877-1Published: 17 November 2019
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XVI, 320
Topics: Operator Theory, Functional Analysis