We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola’s sufficient conditions for conservativity to show that the semigroups are conservative.

In this work we investigate semigroups of operators acting on noncommutative L-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, q-Ornstein-Uhlenbeck semigroups, and the noncommutative Poiss...

We present an abstract method for deriving decay estimates on the resolvents and semigroups of non-symmetric operators in Banach spaces in terms of estimates in another smaller reference Banach space. This applies to a class of operators writing as a regularizing part, plus a dissipative part. The core of the method is a high-order quantitative factorization argument on the resolvents and semig...

We provide sufficient conditions for sums of two unbounded operators on a Banach space to be (pre-)generators of contraction semigroups. Necessary conditions and applications to positive semigroups on Banach lattices are also presented.

As a step toward understanding the analytic behavior of Type-III Ricci flow singularities, i.e. immortal solutions that exhibit |Rm | ≤ C/t curvature decay, we examine the linearization of an equivalent flow at fixed points discovered recently by Baird–Danielo and Lott: nongradient homogeneous expanding Ricci solitons on nilpotent or solvable Lie groups. For all explicitly known nonproduct exam...