Symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras with applications to preserver problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Komuro, Naoto¹  Saito, Kichi-Suke²  Tanaka, Ryotaro^3,4 

[1] Hokkaido Univ, Dept Math, Asahikawa Campus, Asahikawa, Hokkaido 0708621, Japan

[2] Niigata Univ, Inst Sci & Technol, Dept Math Sci, Niigata 9502181, Japan

[3] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

[4] Tokyo Univ Sci, Fac Ind Sci & Technol, Oshamambe, Hokkaido 0493514, Japan

关键词: von Neumann algebra;    (Strong) Birkhoff orthogonality;    Symmetric point;    Linear preserver;   

DOI  :  10.1016/j.jmaa.2018.03.068

来源: Elsevier

【 摘 要 】

Complete characterizations of left or right symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras and abelian unital C*-algebras are given. As an application, we show that every linear strong Birkhoff orthogonality preserver between von Neumann algebras is an algebraic *-isomorphism. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free