We prove for Hermitian matrices (or more generally for completely continuous self-adjoint linear operators in Hilbert space) A and B that Tr (eA+B) ≤ Tr (eAeB). The inequality is shown to be sharper than the convexity property (0 ≤ α ≤ 1) Tr (eαA+(1−α)B) ≤ [Tr (eA)]α[Tr (eB)]1−α, and its possible use for obtaining upper bounds for the partition function is discussed briefly.
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Colin J. Thompson (1965) studied this question.
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