Inequalities

1. Front Matter

   Pages I-IX

   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

      PDF

   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

      PDF

   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

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.

• Coherent States
• Condensed Matter
• Harmonic Map
• Inequalities
• Potential
• STATISTICA
• Stability of Matter
• Statistical Mechanics
• distribution
• functional analysis
• linear optimization
• quantum physics

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)

• 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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