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| 1 | 广义Kato型算子及具有广义(ω)性质算子的摄动显示文摘给出了广义Kato型算子的定义,并根据广义Kato型算子的性质定义了算子的一种新谱,通过该谱给出了Hilbert空间上有界线性算子满足广义(ω)性质的充要条件,并得到了Hilbert空间上有界线性算子在有限秩算子和幂有限秩算子摄动下满足广义(ω)性质的充要条件. | 刘爱芳 曹小红 | 2012 | 吉林大学学报(理学版)2012，50，2： | 1 |
| 2 | (ω')性质和广义(ω')性质的比对显示文摘(ω')性质与广义(ω')性质是Weyl定理的变形。本文利用单值延拓性质、一致Fredholm指标算子和本质谱定义出的一种新的谱集,研究了Hilbert空间上有界线性算子T及其与T可交换的幂有限秩摄动分别有(ω')性质与广义(ω')性质的充要条件。 | 王改玲 曹小红 | 2012 | 山东大学学报(理学版)2012，47，4： | 0 |
| 3 | 一致Fredholm指标算子及广义Weyl型定理显示文摘利用由一致Fredhol m指标性质定义的新谱集σ2(.)研究Hilbert空间上有界线性算子的广义Weyl型定理,得到了T∈B(H)满足广义Weyl型定理的充要条件,同时将主要结论应用到H(p)类算子. | 刘俊英 曹小红 | 2010 | 华中师范大学学报(自然科学版)2010，44，4： | 0 |
| 4 | RIESZ IDEMPOTENT AND BROWDER'S THEOREM FOR ABSOLUTE-(p,r)-PARANORMAL OPERATORS显示文摘An operator T is said to be paranormal if ||T 2x|| ≥ ||T x||2 holds for every unit vector x.Several extensions of paranormal operators are considered until now,for example absolute-k-paranormal and p-paranormal introduced in [10],[14],respectively.Yamazaki and Yanagida [38] introduced the class of absolute-(p,r)-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators.An operator T ∈ B(H) is called absolute-(p,r)-paranormal operator if |||T |p|T |r x||r ≥ |||T |rx||p+r for every unit vector x ∈ H and for positive real numbers p > 0 and r > 0.The famous result of Browder,that self adjoint operators satisfy Browder's theorem,is extended to several classes of operators.In this paper we show that for any absolute-(p,r)paranormal operator T,T satisfies Browder's theorem and a-Browder's theorem.It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-(p,r)-paranormal operator T,then E is self-adjoint if and only if the null space of T μ,N(T μ) N(T μ). | Salah Mecheri | 2012 | Acta Mathematica Scientia2012，32，6： | 0 |
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