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We study Schatten–von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of    L  ∞    spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten–von Neumann estimates in the case of  Haagerup‐like  tensor products.

Multiple operator integrals, Haagerup and Haagerup‐like tensor products, and operator ideals