Complete boundedness of multiple operator integrals

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 asso...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 64; no. 2; pp. 474 - 490
Main Author Coine, Clément
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.06.2021
Cambridge University Press
Subjects
Integrals
Mapping
Operators (mathematics)
Tensors
47B49
operator integrals
multiplier
Complete boundedness
46L07
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439520000570