J4 ›› 2012, Vol. 47 ›› Issue (4): 17-23.
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刘爱芳,李娜娜,曹小红*
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陕西师范大学中央高校基本科研业务费资助项目(GK200901015)
LIU Ai-fang, LI Na-na, CAO Xiao-hong*
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摘要：
给出了广义Kato型的定义,并根据广义Kato型的性质定义了一种新的谱集,然后借助于一致Fredholm指标性质所定义出的谱集给出了Hilbert空间上有界线性算子满足广义(ω′)性质的充要条件,同时讨论了广义(ω′)性质的摄动。另外,利用所得的主要结论,研究了H(p)算子的广义(ω′)性质及其摄动。
关键词: 广义Kato型;广义(ω′)性质;一致Fredholm指标算子;摄动
Abstract:
The definition of the generalized Kato type is given. New spectra are defined in view of the generalized Kato property and the property of consistence in Fredholm and index. The sufficient and necessary conditions are established for a bounded linear operator defined on a Hilbert space for which the generalized property (ω′) holds. Also, the stability of a generalized property (ω′) is discussed. In addition, as a consequence of the main result, the generalized property (ω′) and its perturbation for H(p) operators are studied.
Key words: generalized Kato type; generalized property (ω′); consistent Fredholm and index operators; perturbation
刘爱芳,李娜娜,曹小红*. 广义Kato型及广义(ω′)性质[J]. J4, 2012, 47(4): 17-23.
LIU Ai-fang, LI Na-na, CAO Xiao-hong*. Generalized Kato type and generalized property (ω′)[J]. J4, 2012, 47(4): 17-23.
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http://lxbwk.njournal.sdu.edu.cn/CN/Y2012/V47/I4/17
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