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Abstract characterization of non-associative Orlicz spaces. (Russian) Zbl 0606.46044

Let A be a JBW-algebra admitting a faithful normal finite trace. Given a convex function \(M: {\mathbb{R}}^+\to {\mathbb{R}}^+\) the author defines the corresponding Orlicz space \(L_ M(A)\) in \(L^ 1(A)\). The characterization of Orlicz spaces is based on a structure called Banach ordered Jordan algebroid. No proofs are included.
Reviewer: D.Petz

MSC:

46L70 Nonassociative selfadjoint operator algebras
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46H70 Nonassociative topological algebras