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Inequalities

Selecta of Elliott H. Lieb

  • Book
  • © 2002

Overview

Editors:
  1. Michael Loss

    1. School of Mathematics, Georgia Tech, Atlanta, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. Mary Beth Ruskai

    1. Department of Mathematics, University of Massachusetts Lowell, Lowell, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Essential tool when applying analysis to problems of practical importance

  • Brings together a host of inequalities otherwise scattered in the literature and hard to find

  • Includes supplementary material: sn.pub/extras

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Table of contents (53 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Commentaries

    1. Commentaries

      • Michael Loss, Mary Beth Ruskai
      Pages 1-29

  3. Inequalities Related to Statistical Mechanics and Condensed Matter

    1. Front Matter

      Pages 31-31
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    2. Theory of Ferromagnetism and the Ordering of Electronic Energy Levels

      • Elliott Lieb, Daniel Mattis
      Pages 33-41

    3. Ordering Energy Levels of Interacting Spin Systems

      • Elliott Lieb, Daniel Mattis
      Pages 43-45

    4. Entropy Inequalities

      • Huzihiro Araki, Elliott H. Lieb
      Pages 47-57

    5. A Fundamental Property of Quantum-Mechanical Entropy

      • Elliott H. Lieb, Mary Beth Ruskai
      Pages 59-61

    6. Proof of the strong subadditivity of quantum-mechanical entropy

      • Elliott H. Lieb, Mary Beth Ruskai
      Pages 63-66

    7. Some Convexity and Subadditivity Properties of Entropy

      • Elliott H. Lieb
      Pages 67-79

    8. A Refinement of Simon’s Correlation Inequality

      • Elliott H. Lieb
      Pages 81-89

    9. Two Theorems on the Hubbard Model

      • Elliott H. Lieb
      Pages 91-94

    10. Magnetic Properties of Some Itinerant-Electron Systems at T > 0

      • Elliott H. Lieb, Michael Aizenman
      Pages 95-98

  4. Matrix Inequalities and Combinatorics

    1. Front Matter

      Pages 99-99
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    2. Proofs of some Conjectures on Permanents

      • Elliott H. Lieb
      Pages 101-108

    3. Concavity Properties and a Generating Function for Stirling Numbers

      • Elliott H. Lieb
      Pages 109-112

    4. Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture

      • Elliott H. Lieb
      Pages 113-134

    5. Some Operator Inequalities of the Schwarz Type

      • Elliott H. Lieb, Mary Beth Ruskai
      Pages 135-139

    6. Inequalities for Some Operator and Matrix Functions

      • Elliott H. Lieb
      Pages 141-145

    7. Positive Linear Maps which are Order Bounded on C* Subalgebras

      • Michael Aizenman, E. Brian Davies, Elliott H. Lieb
      Pages 147-149

    8. Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities

      • Eric A. Carlen, Elliott H. Lieb
      Pages 151-170
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Keywords

About this book

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Reviews

From the reviews:

"A well done edition which can be very helpful for mathematicians and mathematical oriented physicists." (Zeitschrift für Analysis und ihre Anwendungen, 22/2, 2003)

"The book contains a list of the publications (276) of E. H. Lieb. There is nicely written introduction ... by the editors. They explain in detail how the selected papers fit into the main directions of Lieb’s research. All together it is a well done edition which can be very helpful for mathematicians and mathematical oriented physicists. The quality of the printing is excellent." (A. Uhlmann, Zeitschrift für Analysis und ihre Anwendungen, Vol. 22 (2), 2003)

Editors and Affiliations

  • School of Mathematics, Georgia Tech, Atlanta, USA

    Michael Loss

  • Department of Mathematics, University of Massachusetts Lowell, Lowell, USA

    Mary Beth Ruskai

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