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

TL;DR

This paper investigates Schatten--von Neumann properties of multiple operator integrals with integrands in Haagerup tensor products, providing sharp estimates and extending results to Haagerup-like tensor products.

Contribution

It introduces sharp Schatten--von Neumann estimates for multiple operator integrals involving Haagerup and Haagerup-like tensor products, advancing the understanding of their operator ideal properties.

Findings

Established sharp Schatten--von Neumann bounds for integrals with Haagerup tensor product integrands.

Extended estimates to Haagerup-like tensor products.

Provided optimal bounds that improve previous results.

Abstract

We study Schatten--von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of $L^\infty$ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten--von Neumann estimates in the case of {\it Haagerup-like} tensor products.