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.
Mots clés
- 46B70
- 17C65 noncommutative L p -spaces
- nonassociative L p -spaces
- projections
- complemented subspaces
- JBW-algebras
- interpolation
- 2020 Mathematics subject classification: Primary 46L51
- 2020 Mathematics subject classification: Primary 46L51 46B70 17C65 noncommutative L p -spaces nonassociative L p -spaces projections complemented subspaces JBW-algebras interpolation
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