Abstract
Let p be an even natural number, \(K\subset l_{p}\) a compact nonempty set and \(L_{n}:C\left( K\right) \rightarrow C\left( K\right) \) a sequence of positive linear operators. We prove that, under suitable assumptions, for every \(f\in C\left( K\right) \), \(\lim \nolimits _{n\rightarrow \infty }L_{n}\left( f\right) =f\) uniformly on K. As applications we give infinite variants of the Bernstein and Kantorovich theorems.
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We would like to thank the reviewer of our paper for carefully reading the manuscript and for such constructive comments, remarks and suggestions which helped improving the first version of the paper.
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Popa, D. Approximation of the continuous functions on \(l_{p}\) spaces with p an even natural number. Positivity 24, 1135–1149 (2020). https://doi.org/10.1007/s11117-019-00725-w
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DOI: https://doi.org/10.1007/s11117-019-00725-w