Anti-norms on finite von Neumann algebras

Jean-Christophe Bourin; Fumio Hiai

Anti-norms on finite von Neumann algebras

Operator Algebras 2015-01-19 v2 Functional Analysis

Authors: Jean-Christophe Bourin , Fumio Hiai

Abstract

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 $\psi$ .

Keywords

von Neumann algebras symmetric anti-norms majorization theory superadditivity inequalities positive operators finite normal trace

Cite

@article{arxiv.1405.2509,
  title  = {Anti-norms on finite von Neumann algebras},
  author = {Jean-Christophe Bourin and Fumio Hiai},
  journal= {arXiv preprint arXiv:1405.2509},
  year   = {2015}
}

Comments

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

Anti-norms on finite von Neumann algebras

Abstract

Keywords

Cite

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