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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.

MSC:
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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