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Complete boundedness of multiple operator integrals

Part of: Selfadjoint operator algebras Special classes of linear operators

Published online by Cambridge University Press:  27 July 2020

Clément Coine
Clément Coine*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha410085, People’s Republic of China
*
e-mail: [email protected]
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Abstract

In this paper, we characterize the multiple operator integrals mappings that are bounded on the Haagerup tensor product of spaces of compact operators. We show that such maps are automatically completely bounded and prove that this is equivalent to a certain factorization property of the symbol associated with the operator integral mapping. This generalizes a result by Juschenko-Todorov-Turowska on the boundedness of measurable multilinear Schur multipliers.

Keywords

Complete boundednessmultiplieroperator integrals

MSC classification

Primary: 46L07: Operator spaces and completely bounded maps 47B49: Transformers, preservers (operators on spaces of operators)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 474 - 490
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

The author is supported by NSFC(11801573).

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