因子von Neumann代数上ξ-斜Jordan可导映射的一个刻画

doi:10.6040/j.issn.1671-9352.0.2020.100

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (7): 32-37.doi: 10.6040/j.issn.1671-9352.0.2020.100

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因子von Neumann代数上ξ-斜Jordan可导映射的一个刻画

张芳娟

西安邮电大学理学院, 陕西西安 710121

发布日期:2020-07-08
作者简介:张芳娟(1976— ), 女, 博士, 副教授, 研究方向为算子代数. E-mail:zhfj888@126.com
基金资助:
国家自然科学基金资助项目(11601420);陕西省自然科学基础研究计划资助项目(2018JM1053)

A characterization of ξ-skew Jordan derivable mappings on factor von Neumann algebras

ZHANG Fang-juan

School of Science, Xian University of Posts and Telecommunications, Xian 710121, Shaanxi, China

Published:2020-07-08

摘要/Abstract

摘要： 设R是维数大于1的因子von Neumann代数。对于给定的复数ξ且ξ≠0,如果映射δ:R→R满足对所有A,B∈R,有δ((A·B)_ξ)=(δ(A)·B)_ξ+(A·δ(B))_ξ,那么δ是可加的*-导子且满足δ(ξA)=ξδ(A)。特别地,若von Neumann代数R是无限的Ⅰ型因子,给出了δ的具体刻画。

关键词: ξ-斜Jordan可导映射, von Neumann代数, *-导子

Abstract: Let R be a factor von Neumann algebra with dim R>1. For given complex number ξ and ξ ≠0, if a map δ:R→R satisfies δ((A·B)_ξ)=(δ(A)·B)_ξ+(A·δ(B))_ξ for all A,B∈R, δ is an additive *-derivation and δ(ξA)=ξδ(A). In particular, if the von Neumann algebra R is infinite type Ⅰ factors, a concrete characterization of δ is given.

Key words: ξ-skew Jordan derivable mapping, von Neumann algebra, *-derivation

中图分类号:

O177.1

张芳娟. 因子von Neumann代数上ξ-斜Jordan可导映射的一个刻画[J]. 《山东大学学报(理学版)》, 2020, 55(7): 32-37.

ZHANG Fang-juan. A characterization of ξ-skew Jordan derivable mappings on factor von Neumann algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 32-37.

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因子von Neumann代数上ξ-斜Jordan可导映射的一个刻画

A characterization of ξ-skew Jordan derivable mappings on factor von Neumann algebras

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