A survey of certain trace inequalities

Volume 30 / 1994

Dénes Petz Banach Center Publications 30 (1994), 287-298 DOI: 10.4064/-30-1-287-298


This paper concerns inequalities like TrA ≤ TrB, where A and B are certain Hermitian complex matrices and Tr stands for the trace. In most cases A and B will be exponential or logarithmic expressions of some other matrices. Due to the interest of the author in quantum statistical mechanics, the possible applications of the trace inequalities will be commented from time to time. Several inequalities treated below have been established in the context of Hilbert space operators or operator algebras. Notwithstanding these extensions our discussion will be limited to matrices.


  • Dénes Petz

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