*-代数上强保持新积的映射

doi:10.6040/j.issn.1671-9352.0.2019.391

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 46-49.doi: 10.6040/j.issn.1671-9352.0.2019.391

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*-代数上强保持新积的映射

张芳娟

西安邮电大学理学院, 陕西西安 710121

发布日期:2019-12-11
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)

Strong new product preserving maps on *-algebras

ZHANG Fang-juan

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

Published:2019-12-11

摘要/Abstract

摘要： 设R是有单位元的*-代数,若R包含非平凡对称幂等元P满足:(1)若ARP={0},则A=0;(2)若AR(I-P)={0},则A=0。设φ:R→R是满射,则φ强保持新积当且仅当存在Z∈Z_S(R)且Z²=I,使得对所有X∈R, 有φ(X)=ZX。作为应用,在没有I₁型的中心直和项的von Neumann代数上和素*-环上得到相似的结果。

关键词: 新积, 保持映射, *-代数

Abstract: Let R be a unital *-algebra with a nontrivial symmetric idempotent P which satisfies:(1)ARP={0} implies A=0;(2)AR(I-P)={0} implies A=0. Let φ:R→R be a surjective map. Then φ is strong new product preserving if and only if there exists an element Z∈Z_S(R)with Z²=I such that φ(X)=ZX for all X∈R. As an application, a characterization of strong new product preserving on von Neumann algebras with no central summands of type I₁ and prime *-ring are obtained.

Key words: new product, preserving map, *-algebra

中图分类号:

O177.1

张芳娟. *-代数上强保持新积的映射[J]. 《山东大学学报(理学版)》, 2019, 54(12): 46-49.

ZHANG Fang-juan. Strong new product preserving maps on *-algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 46-49.

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*-代数上强保持新积的映射

Strong new product preserving maps on *-algebras

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