Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2024

Nonassociative Lp-spaces and embeddings in noncommutative Lp-spaces

Résumé

We define a notion of nonassociative Lp-space associated to a JBW*-algebra (Jordan von Neumann algebra) equipped with a normal faithful state \phi. In the particular case of JW*-algebras underlying von Neumann algebras, we connect these spaces to a complex interpolation theorem of Ricard and Xu on noncommutative Lp-spaces. We also make the link with the nonassociative Lp-spaces of Iochum associated to JBW-algebras and the investigation of contractively complemented subspaces of noncommutative Lp-spaces. More precisely, we show that our nonassociative Lp-spaces contain isometrically the Lp-spaces of Iochum and that all tracial nonassociative Lp-spaces from JW*-factors arise as positively contractively complemented subspaces of noncommutative Lp-spaces.

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Dates et versions

hal-05089847 , version 1 (29-05-2025)

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Cédric Arhancet. Nonassociative Lp-spaces and embeddings in noncommutative Lp-spaces. Journal of Mathematical Analysis and Applications, 2024, 537 (1), pp.128307. ⟨10.1016/j.jmaa.2024.128307⟩. ⟨hal-05089847⟩
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