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数学进展
研究论文
CFI算子和Weyl型定理
CFI Operators and Weyl Type Theorem

戴磊1,2,张建华2,曹小红2,张同琦1
DAI Lei1,2,*, ZHANG Jianhua2, CAO Xiaohong2,ZHANG Tongqi1

1. 渭南师范学院数学与信息科学学院, 渭南, 陕西, 714000;
2. 陕西师范大学数学与信息科学学院, 西安, 陕西, 710062
1. College of Mathematics and Information Science, Weinan Normal University, Weinan, Shaanxi, 714000, P. R. China;
2. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, 710062,P. R. China

收稿日期: 2012-10-18
出版日期: 2014-07-25
DOI: 10.11845/sxjz.2012159b

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摘要 广义$(omega)$性质是Weyl定理的一种变形,它推广了由Rakou{c}evi'{c}在[Matematiu{c}kiVesnik,1985,37(4):423-426]中引入的$(omega)$性质.本文利用一致Fredholm算子指标性质(CFI),给出了Hilbert空间上的有界线性算子满足广义$(omega)$性质的充要条件.另外还利用这一性质考虑了广义$(omega_1)$性质和$(omega_1)$性质的等价性.
关键词 广义$(omega)$性质广义$(omega_1)$性质CFI算子Drazin谱    
Abstract:Generalized property $(omega)$ is a variant of Weyl's theorem which extends property $(omega)$ introduced by Rakou{c}evi'{c} in [{it Matematiu{c}ki Vesnik}, 1985, 37(4): 423-426]. In this paper, using the property of consistency in Fredholm and index (CFI),we establish for a bounded linear operator defined on a Hilbert space a sufficient and necessary condition for which generalized property $(omega)$ holds. In addition, using this property, the equivalence of generalized property $(omega_1)$ and property $(omega_1)$ is considered.
Key wordsgeneralized property $(omega_1)$    CFI operator    Drazin spectrum
基金资助:This work is supported by the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2014JQ1015),the Funding Project on the Key Supporting Subject of Mathematics in Shaanxi Province of China (No.14SXZD003),the Specialized Research Fund for
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