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Noncommutative Köthe duality. (English) Zbl 0801.46074
Summary: Using techniques drawn from the classical theory of rearrangement invariant Banach function spaces we develop a duality theory in the sense of Köthe for symmetric Banach spaces of measurable operators affiliated with a semifinite von Neumann algebra equipped with a distinguished trace. A principal result of the paper is the identification of the Köthe dual of a given Banach space of measurable operators in terms of normality.

46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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