Majoration des semi-groupes de contractions de L1 et applications
Markovian Master Equations. II.
Means of vector-valued functions and projections which commute with the action of a group
Mittelergodische Halbgruppen linearer Operatoren
A semigroup in , a Banach space, is called mean ergodic, if its closed convex hull in has a zero element. Compact groups, compact abelian semigroups or contractive semigroups on Hilbert spaces are mean ergodic.Banach lattices prove to be a natural frame for further mean ergodic theorems: let be a bounded semigroup of positive operators on a Banach lattice with order continuous norm. is mean ergodic if there is a -subinvariant quasi-interior point of and a -subinvariant strictly...
Modal stabilizability and spectral synthesis
Moment sequences and abstract Cauchy problems
We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.
Multiplicative perturbations in semigroup theory with the (Z)-condition.
Multipliers of the Hardy space H¹ and power bounded operators
We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call “shift-bounded”. We show that there is a φ which is a “completely...