Linear combination of projections in von Neumann factors

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Goldstein, Stanislaw¹  Paszkiewicz, Adam¹ 

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

关键词: Projection;    Factor;    Linear combination;   

DOI  :  10.1016/j.jmaa.2020.124135

来源: Elsevier

【 摘 要 】

It is shown that any self-adjoint operator in a finite discrete or infinite von Neumann factor can be written as a real linear combination of 4 projections. On the other hand, in any type II1 algebra and in any type II infinity factor there exists a self-adjoint operator that is not a linear combination of 3 projections. (C) 2020 The Authors. Published by Elsevier Inc.

【 授权许可】

Free