Annals of Functional Analysis

Multivariate extensions of the Golden-Thompson inequality

Frank Hansen

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Abstract

We study concave trace functions of several operator variables and formulate and prove multivariate generalisations of the Golden-Thompson inequality. The obtained results imply that certain functionals in quantum statistical mechanics have bounds of the same form as they appear in classical physics.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 4 (2015), 301-310.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1435764018

Digital Object Identifier
doi:10.15352/afa/06-4-301

Mathematical Reviews number (MathSciNet)
MR3365998

Zentralblatt MATH identifier
1337.15019

Subjects
Primary: 47A63: Operator inequalities
Secondary: 15A45: Miscellaneous inequalities involving matrices

Keywords
Golden-Thompson's trace inequality multivariate trace inequality concave trace function

Citation

Hansen, Frank. Multivariate extensions of the Golden-Thompson inequality. Ann. Funct. Anal. 6 (2015), no. 4, 301--310. doi:10.15352/afa/06-4-301. https://projecteuclid.org/euclid.afa/1435764018


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References

  • T. Ando and F. Hiai, Log majorization and complementary Golden–Thompson type inequalities Linear Algebra Appl. 197-198 (1994), 113–131.
  • T.M. Flett, Differential Analysis, Cambridge University Press, Cambridge, 1980.
  • P.J. Forrester and C.J. Thompson, The Golden–Thompson inequality: Historical aspects and random matrix applications, J. Math. Phys. 55 (2014), no. 2, 023503, 12 pp.
  • S. Golden, Lower bounds for the Helmhotz function, Phys. Rev. B 137 (1965), 1127–1128.
  • F. Hansen and Z. Zhang, Characterisation of matrix entropies, arXiv: 1402.2118v3.
  • F. Hansen, Golden–Thompson's inequality for deformed exponential, J. Stat. Phys. 159 (2015), no. 6, 1300–1305.
  • F. Hiai and D. Petz, The Golden–Thomson trace inequality is complemented, Linear Algebra Appl. 181 (1993), 153–185.
  • E. Lieb, Convex trace functions and the Wigner-Yanase-Dyson conjecture, Advances in Math. 11 (1973), 267–288.
  • E. H. Lieb and R. Seiringer, Stronger subadditivity of entropy, Phys. Rev. A (3) 71 (2005), no. 6, 062329, 9 pp.
  • C.J. Thompson, Inequality with applications in statistical mechanics, J. Math. Phys. 6 (1965), 1812–1813.
  • J.A. Tropp, User-friendly tail bounds for sums of random variables, Found Comput Math. 12 (2012), 389–434.