Derivations and KMS-Symmetric Quantum Markov Semigroups

Abstract We prove that the generator of $$L^2$$ L 2 implementation a KMS-symmetric quantum Markov semigroup can be expressed as square derivation with values in Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups second-named author GNS-symmetric semigroups. This result hinges on introduction new completely positive map algebra bounded operators GNS space. transformation maps to is essential obtain required inner product bimodule.