Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...

In this paper we obtained mean ergodic theorems for semigroups of bounded linear or continuous affine linear operators on a Banach space under non-power bounded conditions. We then apply them to the wave equation and the system of elasticity to show that the mean of their solutions converges to their equilibriums.

We consider perturbations of dynamical semigroups on the algebra all bounded operators in a Hilbert space generated by covariant completely positive measures semi-axis. The construction is based upon unbounded linear generators preadjoint nuclear operators. As an application we construct perturbation semigroup non-unital *-endomorphisms canonical anticommutation relations resulting flow shifts.

We study linear control systems in infinite–dimensional Banach spaces governed by analytic semigroups. For p ∈ [1,∞] and α ∈ R we introduce the notion of L–admissibility of type α for unbounded observation and control operators. Generalising earlier work by Le Merdy [20] and the first named author and Le Merdy [12] we give conditions under which L–admissibility of type α is characterised by bou...

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace correspon...