For quantum Markov semigroups with faithful normal invariant states, the KMS spectral gap is bounded below by the GNS spectral gap, with the result holding for a broad class of inner products from operator monotone functions.
Spectral Analysis for Gaussian Quantum Markov Semigroups
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The KMS and GNS Spectral Gap of Quantum Markov Semigroups
For quantum Markov semigroups with faithful normal invariant states, the KMS spectral gap is bounded below by the GNS spectral gap, with the result holding for a broad class of inner products from operator monotone functions.