Anti-norms on Finite von Neumann Algebras | Zendy

Jean-Christophe Bourin | Zendy; Fumio Hiai | Zendy

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Anti-norms on Finite von Neumann Algebras

Author(s) -

Jean-Christophe Bourin,

Fumio Hiai

Publication year - 2015

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.4171/prims/153

Subject(s) - mathematics , affiliated operator , von neumann architecture , abelian von neumann algebra , pure mathematics , von neumann algebra , algebra over a field , jordan algebra , algebra representation

As the reversed version of usual symmetric norms, we introduce the notion of symmetric anti-norms $\|\cdot\|_!$ 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 $\|\psi(A+B)\|_!\ge\|\psi(A)\|_!+\|\psi(B)\|_!$ for a wide class of functions $\psi$.

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