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Banach空间上一类套代数的李环同构
  • ISSN号：1007-9432
  • 期刊名称：《太原理工大学学报》
  • 时间：0
  • 分类：O177.1[理学—数学;理学—基础数学]
  • 作者机构：太原理工大学数学学院,太原030024
  • 相关基金：国家自然科学基金资助项目（11171249,11271217）
作者： 邓娟[1], 侯晋川[1], 齐霄霏[2]
关键词： 矩阵代数, Lie积, 行列式, 谱, 相似变换, matrix algebras, Lie products, determinants, spectra, similarity transfor- mations
中文摘要：

设M2是二阶复矩阵的全体，圣是M2上的线性映射．本文建立了三阶复正交矩阵与M2上的相似变换之间的一一对应关系，并利用这一对应关系证明了Ф保Lie积行列式（谱、边缘谱）的充要条件是存在c∈{±1，±i），二阶可逆矩阵T和二阶矩阵S，使得Ф（A）=cTAT-1＋tr（SA）I对所有A∈M2都成立．

英文摘要：

Let M2 be the algebra of all 2 × 2 complex matrices and Ф ： M2 → M2 be a linear map. A 1-1 correspondence between the set of 3 × 3 complex orthogonal matrices and the set of similarity transformations of M2 is established, which then is applied to show that Ф preserves the determinant （resp. the spectrum, the peripheral spectrum） of Lie products if and only if there exist a scalarc∈{±1,±i}, matrices S, T ∈ M2 with T invertible, such that Ф（A） = cTAT-1 ＋ tr（SA）I for all A∈ M2.

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算子空间上一般保持问题及在量子信息理论中应用研究
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算子代数上的导子、可乘映射及其在量子逻辑中的应用
期刊论文 41 获奖 2 著作 1
算子代数上的非线性映射及其在量子信息中的应用
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期刊信息
  • 《太原理工大学学报》
  • 中国科技核心期刊
  • 主管单位:山西省教育厅
  • 主办单位:太原理工大学
  • 主编：黄庆学
  • 地址：太原市迎泽西大街79号
  • 邮编：030024
  • 邮箱：tyutxb@tyut.edu.cn
  • 电话：0351-6014376 6014556
  • 国际标准刊号：ISSN：1007-9432
  • 国内统一刊号：ISSN：14-1220/N
  • 邮发代号:22-27
  • 获奖情况:
  • 全国高校学报优秀期刊一等奖、二等奖,国家双效期刊奖,华北十佳期刊优秀奖,山西省一级期刊奖,中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:9375