On some classes of Lototsky-Schnabl operators

Abstract

We study a sequence $( L_n)_{n∈ ℕ}$ of positive operators associated with a sequence $(γ_n)_{n∈ ℕ}$ of real numbers in the unit interval, a lower triangular stochastic matrix P and a positive projection T acting on the space of all continuous functons defined on a convex compact subset of a locally convex Hausdorff space.These operators are particular cases of the so-called Lototsky-Schnabl operators.Under suitable assumptions on $(γ_n)_{n∈ ℕ}, P and T, we investigate the asymptotic properties of the sequence $( L_n)_{n∈ ℕ}$ and of its iterates in connection with the existence of a $C₀$ - semigroup of positive contractions.