The degree of approximation by positive operators on compact connected abelian groups

Walter R. Bloom, Joseph F. Sussich
1982 Journal of the Australian Mathematical Society  
In 1953 P. P. Korovkin proved that if (T n ) is a sequence of positive linear operators defined on the space C of continuous real 2w-periodic functions and lim T n f -f uniformly f o r / = 1, cos and sin, then lim T n f = f uniformly for all / e C. Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of /. We extend this result by giving a quantitative version of
more » ... version of Korovkin's theorem for compact connected abelian groups. 1980 Mathematics subject classification (Amer. Math. Soc): primary 41 A 65, 41 A 25; secondary 41 A 36, 43 A 70.
doi:10.1017/s1446788700018796 fatcat:m3aaa2d3djfr5fdo7t64utulxm