• •

### 有界线性算子的Weyl定理的判定

1. 1.陕西师范大学数学与信息科学学院, 陕西 西安 710119;2.渭南师范学院数理学院, 陕西 渭南 714000
• 收稿日期:2018-03-20 出版日期:2018-10-20 发布日期:2018-10-09
• 作者简介:张莹(1993— ), 女, 硕士研究生, 研究方向为算子理论. E-mail:zhangying12240705@snnu.edu.cn*通信作者简介:曹小红(1972— ), 女, 教授, 博士生导师, 研究方向为算子理论. E-mail:xiaohongcao@snnu.edu.cn
• 基金资助:
国家自然科学基金资助项目(11471200;11501419);陕西师范大学中央高校基本科研业务费专项资金资助项目(GK201601004);渭南市科技计划资助项目(2016KYJ-3-3);渭南师范学院自然科学人才资助项目(15ZRRC10)

### Judgement of Weyls theorem for bounded linear operators

ZHANG Ying1, CAO Xiao-hong1*, DAI Lei2

1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China;
2. College of Mathematics and Physics, Weinan Normal University, Weinan 714000, Shaanxi, China
• Received:2018-03-20 Online:2018-10-20 Published:2018-10-09

Abstract: Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. T∈B(H) satisfies Weyls theorem if σ(T)\σw(T)=π00(T), where σ(T) and σw(T) denote the spectrum and the Weyl spectrum respectively, π00(T)={λ∈iso σ(T):0An operator T∈B(H) is said to have the single-valued extension property, if for every open set U⊆C, the only analytic solution of the equation (T-λI)f(λ)=0(for all λ∈U)is zero function on U. Using the single-valued extension property, we give a new judgement for Weyls theorem.

• O177.2
 [1] WEYL H V. Über beschränkte quadratische Formen, deren Differenz vollstetig ist[J]. Rendiconti Del Circolo Matematico Di Palermo, 1909, 27(1):373-392. [2] BERBERIAN S K. An extension of Weyls theorem to a class of not necessarily normal operators[J]. Michigan Mathematical Journal, 1969, 16(3):273-279. [3] LI Chunguang, ZHU Sen, FENG Youling. Weyls theorem for functions of operators and approximation[J]. Integral Equations and Operator Theory, 2010, 67(4):481-497. [4] CURTO R E, HAN Y M. Weyls theorem for algebraically paranormal operators[J]. Integral Equations and Operator Theory, 2003, 47(3):307-341. [5] AN I J, HAN Y M. Weyls theorem for algebraically quasi-class a operators[J]. Integral Equations and Operator Theory, 2008, 62(1):1-10. [6] SHI Weijuan, CAO Xiaohong. Weyls theorem for the square of operator and perturbations[J]. Communications in Contemporary Mathematics, 2015, 17:1450042. [7] COBURN L A. Weyls theorem for nonnormal operators[J]. Michigan Mathematical Journal, 1966, 13(3):285-288. [8] DUGGAL B P. The Weyl spectrum of p-hyponormal operators[J]. Integral Equations and Operator Theory, 1997, 29(2):197-201. [9] CAO Xiaohong. Analytically class operators and Weyls theorem[J]. Journal of Mathematical Analysis and Applications, 2006, 320(2):795-803. [10] DUNFORD N. Spectral operator[J]. Pacific Journal of Mathematics, 1954, 4(3):321-354. [11] FINCH J K. The single valued extension property on a Banach space[J]. Pacific Journal of Mathematics, 1975, 58(1):61-69. [12] ZHU Sen, LI Chunguang. SVEP and compact perturbations[J]. Journal of Mathematical Analysis and Applications, 2011, 380(1):69-75. [13] Aiena P, Peña P. Variantions on Weyls theorem[J]. Journal of Mathematical Analysis and Applications, 2006, 324(1):566-579. [14] AMOUCH M. Weyl type theorem for operators satisfying the single-valued extention property[J]. Journal of Mathematical Analysis and Applications, 2007, 326(2):1476-1484. [15] DUGGAL B P. Upper triangular operator matrices, SVEP and Browder, Weyl theorems[J]. Integral Equations and Operator Theory, 2009, 63(1):17-28. [16] 江泽坚, 吴智泉, 纪友清. 实变函数论[M]. 3版. 北京: 高等教育出版社, 2007: 17-42. JIANG Zejian, WU Zhiquan, JI Youqing. Real variable function theory[M]. 3rd ed. Beijing: Higher Education Press, 2007: 17-42. [17] TAYLOR A E. Theorems on ascent, descent, nullity and defect of linear operators[J]. Mathematische Annalen, 1996, 163(1):18-49.
 [1] 刘艳芳,王玉玉. Adams谱序列E2项的一些注记[J]. 山东大学学报（理学版）, 2018, 53(8): 43-48. [2] 于倩倩,魏广生. Jacobi矩阵的逆谱问题及其应用[J]. 山东大学学报（理学版）, 2018, 53(8): 66-76. [3] 林穗华. Wolfe线搜索下的修正FR谱共轭梯度法[J]. 山东大学学报（理学版）, 2017, 52(4): 6-12. [4] 宋佳佳,曹小红,戴磊. 上三角算子矩阵SVEP微小紧摄动的判定[J]. 山东大学学报（理学版）, 2017, 52(4): 61-67. [5] 戴磊,曹小红. (z)性质与Weyl型定理[J]. 山东大学学报（理学版）, 2017, 52(2): 60-65. [6] 孔莹莹,曹小红,戴磊. a-Weyl定理的判定及其摄动[J]. 山东大学学报（理学版）, 2017, 52(10): 77-83. [7] 王国辉, 杜小妮, 万韫琦, 李芝霞. 周期为pq的平衡四元广义分圆序列的线性复杂度[J]. 山东大学学报（理学版）, 2016, 51(9): 145-150. [8] 董炯,曹小红. 算子立方的Weyl定理及其紧摄动[J]. 山东大学学报（理学版）, 2016, 51(8): 15-21. [9] 刘玉梅,王海蓉,刘淑芳. 荧光光谱法研究羟基化单壁碳纳米管与牛血清白蛋白/血红蛋白的相互作用[J]. 山东大学学报（理学版）, 2016, 51(3): 29-33. [10] 马飞翔,廖祥文,於志勇,吴运兵,陈国龙. 基于知识图谱的文本观点检索方法[J]. 山东大学学报（理学版）, 2016, 51(11): 33-40. [11] 吴学俪, 曹小红, 张敏. 有界线性算子的单值扩张性质的摄动[J]. 山东大学学报（理学版）, 2015, 50(12): 5-9. [12] 杨功林, 纪培胜. Hilbert C*-模中本原理想子模的一些性质[J]. 山东大学学报（理学版）, 2014, 49(10): 50-55. [13] 崔苗苗, 王碧玉, 曹小红. 算子矩阵的一个注记[J]. 山东大学学报（理学版）, 2014, 49(10): 56-61. [14] 李超,赵丽娟,张瑶,任冬梅*. HPLC法直接拆分dracocephins A对映异构体[J]. 山东大学学报（理学版）, 2014, 49(1): 36-38. [15] 赵军胜1,2，王秀丽1,2，高明伟1,2，王家宝1,2，王永翠1,2，陈莹1,2，姜辉1,2，杨静1,2，王留明1,2*. 红花性状标记杂交棉新品种鲁05H9 SSR#br# 指纹图谱构建及应用[J]. 山东大学学报（理学版）, 2014, 49(1): 44-49.
Viewed
Full text

Abstract

Cited

Shared
Discussed