# Positive linear operators and the approximation of continuous functions on locally compact abelian groups

Bloom, W.R. and Sussich, J.F.
(1980)
*Positive linear operators and the approximation of continuous functions on locally compact abelian groups.*
Journal of the Australian Mathematical Society (Series A), 30
(2).
pp. 180-186.

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## Abstract

In 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2π-periodic functions and limn→r Tnf = f uniformly for f = 1, cos and sin. then limn→r Tnf = f uniformly for all fxs2208C. We extend this result to spaces of continuous functions defined on a locally compact abelian group G, with the test family {1, cos, sin} replaced by a set of generators of the character group of G.

Item Type: | Journal Article |
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Murdoch Affiliation: | School of Mathematical and Physical Sciences |

Publisher: | Cambridge University Press |

Copyright: | © 1980 Australian Mathematical Society |

URI: | http://researchrepository.murdoch.edu.au/id/eprint/31418 |

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