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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.

Link to Published Version: http://dx.doi.org/10.1017/S1446788700016475
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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.

Publication Type: Journal Article
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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