[1]宋显花.B(H)上保持*-拟积的双射[J].四川师范大学学报(自然科学版),2019,(05):667-673.[doi:10.3969/j.issn.1001-8395.2019.05.015]
 SONG Xianhua.A Bijection Preserving *-quasi-product on B(H)[J].Journal of SichuanNormal University,2019,(05):667-673.[doi:10.3969/j.issn.1001-8395.2019.05.015]
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B(H)上保持*-拟积的双射()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
667-673
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
A Bijection Preserving *-quasi-product on B(H)
文章编号:
1001-8395(2019)05-0667-07
作者:
宋显花
青海师范大学 数学与统计学院, 青海 西宁 810008
Author(s):
SONG Xianhua
College of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai
关键词:
算子代数 保持 拟积 同构
Keywords:
operators algebra preserve quasi-product isomorphism
分类号:
O177.1
DOI:
10.3969/j.issn.1001-8395.2019.05.015
文献标志码:
A
摘要:
设B(H)是维数大于1的复Hilbert空间H上有界线性算子全体得到的代数.A,B∈B(H),定义拟积AB=A+B-AB.证明φ是B(H)上的双射且满足φ(A*B)=φ(A)*φ(B), A,B∈B(H)的充要条件是当dim H≥3时,存在H上的酉算子或共轭酉算子U使得φ(A)=UAU*,A∈B(H); 当dim H=2时,存在H上的酉算子U使得φ(A)=UAτU*,A∈B(H),其中τ是C上的环自同构.设A=(aij)∈M2,则令Aτ=τ(aij).
Abstract:
Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H with dim H≥2.For any A,B∈B(H), define the quasi-product of A and B as A B=A+B-AB.It is proved that a bijection φ on B(H)satisfys φ(A* B)=φ(A)* φ(B)for all A,B in B(H) if and only if there is a unitary or an anti-unitary operator U on H such that φ(A)=UAU* for all A in B(H).When dim H≥3 or there is a unitary operator U on H such that φ(A)=UAτU* for all A in B(H) when dim H=2, where τ is a ring automorphism on C and Aτ=τ(aij) for all A=(aij)in M2.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-02-24 接受日期:2019-03-21
基金项目:青海省科技厅项目(2018-ZJ-925Q和2017-ZJ-790)
作者简介:宋显花(1981—),女,副教授,博士,主要从事算子理论与算子代数的研究,E-mail:songxianhua20@126.com
更新日期/Last Update: 2019-07-15