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Let {Tn}n be a sequence of bounded linear operators on L∞ such that ‖Tn‖ → 1 and ‖Tng − g‖∞ → 0 for every g ∈ QC. It is proved that ‖Tnf − f‖∞ → 0 for every f ∈ L∞.

Sequential type Korovkin theorem on 𝐿^{∞} for QC-test functions