The adjoint of a positive semigroup
نویسنده
چکیده
© Foundation Compositio Mathematica, 1994, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
منابع مشابه
Adjoints of Solution Semigroups and Identifiability of Delay Differential Equations in Hilbert Spaces
The paper deals with semigroups of operators associated with delay differential equation: ẋ(t) = Ax(t) + L1x(t− h) + L2xt, where A is the infinitesimal generator of an analytic semigroup on a Hilbert space X and L1, L2 are densely defined closed operators in X and L2(−h, 0;X) respectively. The adjoint semigroup of the solution semigroup of the delay differential equation is characterized. Eigen...
متن کاملOrnstein-Uhlenbeck and renormalization semigroups
The Ornstein-Uhlenbeck semigroup combines Gaussian diffusion with the flow of a linear vector field. In infinite dimensional settings there can be non-Gaussian invariant measures. This gives a context for one version of the renormalization group. The adjoint of the OrnsteinUhlenbeck semigroup with respect to an invariant measure need not be an Ornstein-Uhlenbeck semigroup. This adjoint is the a...
متن کاملInteraction representation method for Markov master equations in quantum optics
Conditions sufficient for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators. The order of the Hamiltonian may be higher than the order of completely positive part of the formal generator of a QDS. The unital property of a minimal qua...
متن کاملR-diagonal Dilation Semigroups
This paper addresses extensions of the complex Ornstein-Uhlenbeck semigroup to operator algebras in free probability theory. If a1, . . . , ak are ∗-free R-diagonal operators in a II1 factor, then Dt(ai1 · · · ain) = e −ntai1 · · · ain defines a dilation semigroup on the non-self-adjoint operator algebra generated by a1, . . . , ak. We show that Dt extends (in two different ways) to a semigroup...
متن کاملGenerators of Detailed Balance Quantum Markov Semigroups
For a quantum Markov semigroup T on the algebra B(h) with a faithful invariant state ρ, we can define an adjoint T̃ with respect to the scalar product determined by ρ. In this paper, we solve the open problems of characterising adjoints T̃ that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators H,Lk in the Gorini Kossakowski Sudarshan Lindblad...
متن کامل1 3 Ja n 20 06 Second - order operators with degenerate coefficients
We consider properties of second-order operatorsH = − ∑d i,j=1 ∂i cij ∂j on R with bounded real symmetric measurable coefficients. We assume that C = (cij) ≥ 0 almost everywhere, but allow for the possibility that C is singular. We associate with H a canonical self-adjoint viscosity operator H0 and examine properties of the viscosity semigroup S generated by H0. The semigroup extends to a posit...
متن کامل