Complete boundedness of multiple operator integrals

Coine, Clément

doi:10.4153/s0008439520000570

Cited by 1 publication

(1 citation statement)

References 15 publications

(10 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After a first version of this paper was circulated in 2017, some of its results have been used in [9,10,13,25,38]. BIBLIOGRAPHY…”

Section: Added April 2020mentioning

confidence: 99%

When do triple operator integrals take value in the trace class?

Coine¹,

Merdy²,

Sukochev³

2022

Annales De l'Institut Fourier

Self Cite

View full text Add to dashboard Cite

Consider three normal operators A, B, C on a separable Hilbert space H as well as scalar-valued spectral measures λ A on σ(A), λ B on σ(B) and λ C on σ(C). For any φ ∈ L ∞ (λ A × λ B × λ C ) and any X, Y ∈ S 2 (H), the space of Hilbert-Schmidt operators on H, we provide a general definition of a triple operator integral Γ A,B,C (φ)(X, Y ) belonging to S 2 (H) in such a way that Γ A,B,C (φ) belongs to the space B 2 (S 2 (H) × S 2 (H), S 2 (H)) of bounded bilinear operators on S 2 (H), and the resulting mappinginto S 1 (H), the space of trace class operators on H, if and only if it has the following factorization property: there exist a Hilbert space H and two func-. This is a bilinear version of Peller's Theorem characterizing double operator integral mappings S 1 (H) → S 1 (H). In passing we show that for any separable Banach spaces E, F , any w *measurable esssentially bounded function valued in the Banach space Γ 2 (E, F * ) of operators from E into F * factoring through Hilbert space admits a w * -measurable Hilbert space factorization.Résumé. -Considérons trois opérateurs normaux A, B, C sur un espace de Hilbert séparable H ainsi que des mesures spectrales scalairesH)) est une isométrie w * -continue. On montre alors qu'étant donnée une fonction φ ∈ L ∞ (λ A × λ B × λ C ), Γ A,B,C (φ) envoie S 2 (H) × S 2 (H) dans S 1 (H), l'espace des opérateurs à trace sur H, si et seulement si φ vérifie

show abstract

“…After a first version of this paper was circulated in 2017, some of its results have been used in [9,10,13,25,38]. BIBLIOGRAPHY…”

Section: Added April 2020mentioning

confidence: 99%