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.
The H aagerup approximation property for von N eumann algebras via quantum M arkov semigroups and D irichlet forms
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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.