Anti-norms on finite von Neumann algebras

2014/05/11 by Jean-Christophe Bourin, Bourin, Jean-Christophe, Fumio Hiai +1
Mathematics · #46L51 #46L52 #47A30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L51 #msc:46L52 #msc:47A30

paper · pdf · doi:10.48550/arxiv.1405.2509

27 pages, largely revised from the previous version, to appear in Publ. Res. Inst. Math. Sci

arxiv created 2015/01/16 · arxiv updated 2015/01/19

Abstract

As the reversed version of usual symmetric norms, we introduce the notion of symmetric anti-norms ‖⋅‖_! defined on the positive operators affiliated with a finite von Neumann algebra with a finite normal trace. Related to symmetric anti-norms, we develop majorization theory and superadditivity inequalities of the form ‖ψ(A+B)‖_!≥‖ψ(A)‖_!+‖ψ(B)‖_! for a wide class of functions ψ.

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