Von Neumann Algebra Preduals Satisfy the Linear Biholomorphic Property

DOI10.7146/MATH.SCAND.A-23689zbMATH Open1362.46060arXiv1309.0982OpenAlexW2963175757MaRDI QIDQ3187165

László Stachó, Antonio M. Peralta

Publication date: 16 August 2016

Published in: MATHEMATICA SCANDINAVICA (Search for Journal in Brave)

Abstract: We prove that for every JBW${*}^{}$-triple $E$ of rank $>1$, the symmetric part of its predual reduces to zero. Consequently, the predual of every infinite dimensional von Neumann algebra $A$ satisfies the linear biholomorphic property, that is, the symmetric part of $A_{*}$ is zero. This solves a problem posed by M. Neal and B. Russo in [Mathematica Scandinavica, to appear]

Full work available at URL: https://arxiv.org/abs/1309.0982

zbMATH Keywords

von Neumann algebrasbiholomorphical equivalenceJBW\(^\ast\)-triplesymmetric part of the predual of a von Neumann algebra

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) General theory of von Neumann algebras (46L10) Nonassociative selfadjoint operator algebras (46L70)

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