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

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. © 2017 London Mathematical Society.