Vol. 63, No. 1, 1976

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Korovkin approximations in Lp-spaces

William George Kitto and Daniel Eliot Wulbert

Vol. 63 (1976), No. 1, 153–167

The main result is a characterization of finite Korovkin sets for positive operators in lp. It follows that a finite set containing a positive function is a Korovkin set in lp if and only if it is a Korovkin set in c0. The methods also show:

Proposition. Let X be a compact subset of Rn. Let K be a subspace of C(X) containing the constants. If K is a Korovkin set in C(X), then K is Korovkin set in Lp(X).

Several related results are also given. For example a question of G. G. Lorentz about the restrictions of Korovkin set in C(X) to a subset Y X is answered.

Mathematical Subject Classification 2000
Primary: 41A65
Received: 11 July 1973
Revised: 15 July 1974
Published: 1 March 1976
William George Kitto
Daniel Eliot Wulbert