The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra is established providing a natural decomposition of a Markovian open quantum system into its noiseless (decoherencefree) and irreducible (ergodic) components. This leads to a new characterisation of the structure of invariant states and a new method for finding decoherence-free subsystems and subspaces. Examples are presented to illustrate these results.

In this paper we study the boundedness of spectral multipliers associated to the multidimensional Laguerre operator L α . It is well known that, for special values of α, the analysis of the Laguerre operator can be interpreted as the analysis of the Ornstein-Uhlenbeck operator acting on "polyradial" functions. Exploiting this relation, we prove that if M is a bounded holomorphic function in the sector S = {z ∈ C : | arg z| < arcsin |2/p − 1|}, satisfying suitable Hörmander type conditions on the boundary, then the spectral operator M(L α ) is bounded on L p with respect to the Laguerre measure. We also prove that holomorphy in the sector S is a necessary condition for multipliers whose norm is invariant under dilations. (2000): 47A60, 42B15, 47D03 Mathematics Subject Classification

We prove hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup on the entire algebra B(h) of bounded operators on a separable Hilbert space h. We exploit the particular structure of the spectrum together with hypercontractivity of the corresponding birth and death process and a proper decomposition of the domain. Then we deduce a logarithmic Sobolev inequality for the semigroup and gain an elementary estimate of the best constant.

We study environmental decoherence for a quantum Markov semigroup T acting on\ud an arbitrary von Neumann algebra M. In particular, we analyze the relationships\ud between the decomposition of the algebra induced by decoherence and a sort of\ud “isometric-sweeping decomposition” for the space of states. Moreover, when the\ud semigroup has a faithful normal invariant state, we embed the algebra M in its\ud completion \hat{M} with respect to the scalar product induced by the faithful state,\ud and we compare the decomposition induced by decoherence with some other kind\ud of isometric-sweeping decompositions of M and \hat{M}

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