Vol. 63, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Vol. 315: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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