The Equivalence between Property (ω) and Weyl’s Theorem

The Equivalence between Property (ω) and Weyl’s Theorem

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摘要 We call T C B（H） consistent in Fredholm and index （briefly a CFI operator） if for each B ∈ B（H）, TB and BT are Fredholm together and the same index of B, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl＇s theorem and property （ω） for T and its conjugate operator T^＊. In addition, the property （ω） for operator matrices is considered. We call T C B（H） consistent in Fredholm and index （briefly a CFI operator） if for each B ∈ B（H）, TB and BT are Fredholm together and the same index of B, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl＇s theorem and property （ω） for T and its conjugate operator T^＊. In addition, the property （ω） for operator matrices is considered.

作者 Ling Ling ZHAO Xiao Hong CAO He Jia ZHANG

机构地区 College of Mathematics and Information Science

出处《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期705-712,共8页 数学研究与评论（英文版）

基金 Supported by Plan of the New Century Talented Person of the Ministry of Education of China (Grant No.NCET-06-0870) the Fundamental Research Funds for the Central Universities (Grant GK200901015)

关键词 Weyl＇s theorem property （ω） SPECTRUM Weyl＇s theorem property （ω） spectrum

分类号 O177.2 [理学—基础数学]

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1AIENA P, PENA P. Variations on Weyl's theorem [J]. J. Math. Anal. Appl., 2006, 324(1): 566-579.
2BERBERIAN S K. An extension of Weyl's theorem to a class of not necessarily normal operators [J]. Michigan Math. J., 1969, 16: 273-279.
3CAO Xiaohong. Weyl spectrum of the products of operators [J]. J. Korean Math. Soc., 2008, 45(3): 771-780.
4BERBERIAN S K. The Weyl spectrum of an operator [J]. Indiana Univ. Math. J., 1970/1971, 20: 529-544.
5COBURN L A. Weyl's theorem for nonnormal operators [J]. Michigan Math. J., 1966, 13: 285-288.
6HARTE R. Invertibility and Singularity for Bounded Linear Operators [M]. Marcel Dekker, Inc., New York, 1988.
7HARTE R. Fredholm, Weyl and Browder theory [J]. Proc. Roy. Irish Acad. Sect. A, 1985, 85(2): 151-176.
8HARTE R, LEE W Y. Another note on Weyl's theorem [J]. Trans. Amer. Math. Soc., 1997, 349(5): 2115-2124.
9ISTRATESCU V I. On Weyl's spectrum of an operator (I) [J]. Rev. Roumaine Math. Pures Appl., 1972, 17: 1049-1059.
10OBERAI K K. On the Weyl spectrum [J]. Illinois J. Math., 1974, 18: 208-212.

1刘华珂,王天芹.光滑Weyl和的分数幂均值的数值上界(Ⅱ)[J].数学年刊（A辑）,2014,35(5):523-532.
2王天芹,刘华珂.光滑Weyl和的分数幂均值的数值上界[J].数学学报（中文版）,2014,57(1):199-208. 被引量：1
3孙翼,井思聪,阮图南.Weyl编序下玻色弦的量子化[J].高能物理与核物理,1989,13(5):411-418.
4The equivalence between two types of exponential stabilities[J].Chinese Science Bulletin,1998,43(18):1583-1584.
5赵克全,陈哲,杨新民.The Equivalence about Strongly Pseudoinvexity and Strongly Invariant Pseudomonotonicity[J].Chinese Quarterly Journal of Mathematics,2011,26(4):608-612.
6刘全慧,俞文光.Weyl本征微分和连续定态体系的精确不确定关系(英文)[J].黑龙江大学自然科学学报,1993,10(2):69-74.
7朱宝彦.Weyl极限点的映射定理[J].沈阳建筑大学学报（自然科学版）,1995,19(3):285-288. 被引量：1
8Liping Yang.The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space[J].Numerical Mathematics A Journal of Chinese Universities(English Series),2007,16(1):83-91.
9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.
10范洪义,胡利云,袁洪春.The s-parameterized Weyl-Wigner correspondence in the entangled form and its applications[J].Chinese Physics B,2010,19(6):52-57.

Journal of Mathematical Research and Exposition

2011年第4期

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The Equivalence between Property (ω) and Weyl’s Theorem

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