Nonassociative L^p-spaces and embeddings in noncommutative L^p-spaces

2023/07/10 by Arhancet, Cédric
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2307.04452

Abstract

We define a notion of nonassociative L^p-space associated to a JBW^*-algebra (Jordan von Neumann algebra) equipped with a normal faithful state φ. 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 L^p-spaces. We also make the link with the nonassociative L^p-spaces of Iochum associated to JBW-algebras and the investigation of contractively complemented subspaces of noncommutative L^p-spaces. More precisely, we show that our nonassociative L^p-spaces contain isometrically the L^p-spaces of Iochum and that all tracial nonassociative L^p-spaces from JW^*-factors arise as positively contractively complemented subspaces of noncommutative L^p-spaces.

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