Limit semigroups of Bernstein-Schnabl operators associated with positive projections
Corrigendum to ``Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness'' (Boll. U.M.I (9) II (2009), 135-150)
Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness
Of concern are Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. With respect to these sequences of positive linear operators we determine the classes of all continuous functions verifying a pointwise asymptotic formula or a uniform one. Our methods are essentially based on a general characterization of the domains of Feller semigroups in terms of asymptotic formulae and on the determination of both the saturation class of Bernstein-Schnabl...
Lipschitz Contractions, Unique Ergodicity and Asymptotics of Markov Semigroups
We are mainly concerned with the asymptotic behaviour of both discrete and continuous semigroups of Markov operators acting on the space of all continuous functions on a compact metric space . We establish a simple criterion under which such semigroups admit a unique invariant probability measure on that determines their limit behaviour on and on . The criterion involves the behaviour of the semigroups on Lipschitz continuous functions and on the relevant Lipschitz seminorms. Finally,...
Regular vector lattices of continuous functions and Korovkin-type theorems-Part I
We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive...
Regular vector lattices of continuous functions and Korovkin-type theorems-Part II
By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive projections....
On some density theorems in regular vector lattices of continuous functions.
In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions de ned on a locally compact Hausdorff space, which we introduced and studied in [3,4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the so-called generalized af ne functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by...
Positive operators and approximation in function spaces on completely regular spaces.
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