The orthogonal projection onto Helson matrices, and every multiplicative weighted version of it, is unbounded on the Schatten class S_q for every 1 ≤ q ≠ 2 < ∞.
Guichardet, Tensor products of C∗ -algebras, part II: Infinite tensor products , Aarhus Universitet Lecture Notes Series, no
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Projecting onto Helson matrices in Schatten classes
The orthogonal projection onto Helson matrices, and every multiplicative weighted version of it, is unbounded on the Schatten class S_q for every 1 ≤ q ≠ 2 < ∞.