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Regular vector lattices of continuous functions and Korovkin-type theorems-Part II

Francesco Altomare, Mirella Cappelletti Montano (2006)

Studia Mathematica

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....

Remarks on an article of J.P. King

Heiner Gonska, Paula Piţul (2005)

Commentationes Mathematicae Universitatis Carolinae

The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized.

Representation formulae for (C₀) m-parameter operator semigroups

Mi Zhou, George A. Anastassiou (1996)

Annales Polonici Mathematici

Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.

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