A nonlinear characterization of type I factors based on strong Birkhoff–James orthogonality

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Abstract

A nonlinear characterization of type I factors among von Neumann algebras based on strong Birkhoff–James orthogonality is given. As an application, it is shown that if a von Neumann algebra is isomorphic to a type I factor with respect to the structure of strong Birkhoff–James orthogonality, then they are ∗ -isomorphic as von Neumann algebras.

Original languageEnglish
Article number29
JournalAnnals of Functional Analysis
Volume13
Issue number2
DOIs
Publication statusPublished - Apr 2022

Keywords

  • Nonlinear classification
  • Strong Birkhoff–James orthogonality
  • Type I factor
  • von Neumann algebra

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