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On a submajorization inequality of T. Ando. (English) Zbl 0826.46054

Huijsmans, C. B. (ed.) et al., Operator theory in function spaces and Banach lattices. Essays dedicated to A. C. Zaanen on the occasion of his 80th birthday. Symposium, Univ. of Leiden, NL, September 1993. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 75, 113-131 (1994).
Summary: A submajorization inequality of T. Ando for operator monotone functions is extended to the setting of measurable operators affiliated with a semifinite von Neumann algebra. The general form yields certain norm inequalities for the absolute value in symmetric operator spaces which were previously known in the setting of trace ideals.
For the entire collection see [Zbl 0949.47500].

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.)
47A63 Linear operator inequalities
47B65 Positive linear operators and order-bounded operators
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