Noncommutative Köthe duality. (English) Zbl 0801.46074

Dodds, Peter G.; Dodds, Theresa K.-Y.; de Pagter, Ben

Trans. Am. Math. Soc. 339, No. 2, 717-750 (1993).

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.)

Keywords:

rearrangement invariant Banach function spaces; symmetric Banach spaces of measurable operators; affiliated with a semifinite von Neumann algebra equipped with a distinguished trace; Köthe dual of a given Banach space of measurable operators