基本情况

曹小红，女，教授，博士，博士研究生导师，毕业于北京大学。目前主要从事算子理论与算子代数研究，2006年入选教育部“新世纪优秀人才支持计划”，先后主持完成国家自然科学基金数学天元基金项目一项，教育部新世纪优秀人才支持计划项目一项，国家自然科学基金面上项目一项(No.11471200)。在国内外重要期刊上发表高质量论文100余篇，文章主要发表在“Journal of Mathematical Analysis   and Applications”， “Linear Algebra and its  Application”， “Proceedings of the  American Mathematical Society”，“Studia Mathematica”， “Communications in Contemporary Mathematics”等期刊上。2010年在高教出版社出版书籍《算子与框架理论》，2014年获陕西高等学校科学技术一等奖。

代表性学术论文

• [1] Jiong Dong, Xiaohong Cao, Compact perturbations of both SVEP and Weyl‘s theorem for 3x3 upper triangular operator matrices,Linear and Multilinear algebra, 2020, 68(10), 2020-2033.
  

• [2] Jiong Dong, Xiaohong Cao, The (generalized) Weylness of upper triangular operator matrices, Analysis Mathematica, 2020, 46(3), 465-481.

• [3] Jiong Dong, Xiaohong Cao, On Weyl's theorem for functions of operators, Acta Mathematica Sinica, 2019,35(8), 1367-1376.

• [4] Xiaohong Cao,Jiong Dong, Junhui Liu, Weyl's theorem and its perturbations for the functions of operators, Operator and Matrices, 2018, 12(4), 1145-1157.

• [5] Miaomiao Cui, Xiaohong Cao, Weyl's theorem for upper triangular operator matrix and perturbations, Linear and Multilinear algebra, 2018, 1(1), 1-12.

• [6] Jiong Dong, Xiaohong Cao, Junhui Liu, A-Weyl’s theorem and its perturbation, Acta Mathematica Sinica, 2017, 60(6), 1-12.

• [7] Weijuah Shi, Xiaohong Cao, Weyl's theorem for the square of operator and perturbations, Communications in Contemporary Mathematics, 2015, 17(5), 42375.

• [8] Weijuah Shi, Xiaohong Cao, Property (w) and its perturbations, Acta Mathematica Sinica, 2014, 30(5), 797-804.

• [9] Xiaohong Cao, Shizhao Chen, Linear maps between operator algebras preserving certain spectral functions, Banach Journal of Mathematical Analysis, 2014, 8(1), 39-46.

• [10] Xiaohong Cao, Lei Dai, The stability of the single valued extension property, Journal of Mathematical Analysis and Applications, 2012, 390, 368-373.

• [11] Xiaohong Cao, Aifang Liu, Generalized Kato type and perturbations for property (w), Linear Algebra and its Applications, 2012(436), 2231-2239.

• [12] Xiaohong Cao, Hejia Zhang, Yanhua Zhang, Consistent invertiblity and Weyl’s theorem, Journal of Mathematical Analysis and Applications, 2010, 369, 258-264.

• [13] Xiaohong Cao, Chenhui Sun, Lei Dai, Property (w) and Weyl type theorem, Journal of Mathematical Analysis and Applications, 2010, 363(1), 1-6.

• [14] 孟彬,曹小红,《算子与框架教程》，高等教育出版社, 2010.

教育科研项目

• 1. 2007.1至2009.12，对谱理论中若干问题的研究，教育部新世纪优秀人才支持计划资助项目；
  

• 2. 2008.1至2008.12，基于量子力学的算子论研究，国家自然科学基金数学天元基金；

• 3.  2015.1至2018.12，线性算子的谱结构及其扰动，国家自然科学基金面上项目。

教育科研奖励

• 主持完成的《局部谱的稳定性及其在量子纠错码构造中的应用》获陕西高等学校科学技术奖励一等奖。

讲授课程

• 本科生：《数学分析》 。

• 研究生：《现代分析》《谱理论》《Banach代数技巧》。