扩展Rakočević的财产
Extended Rakočević's property
摘要：
本文的目的是引入和研究Rakočević的性质$(w)$和Berkani-Zariouh在\cite{berkani-zariouh1}中引入的性质$(b)$的新推广，并结合其它Weyl型定理和最近的性质.我们特别证明了以下两个结果：1.有界线性算子$T$满足性质$(w_{π_{00}})$当且仅当$T$满足性质$(w)$和$σ_{uf}(T)=σ_{uw}(T).$ 2。$T$满足性质$(gw_{π_{00}})$当且仅当$T$满足性质$(w_{π_{00}})$，并且$π_{0}(T)=p_{0}^a(T).$运算符类被认为是说明性示例。
英文摘要：
The purpose of this paper is to introduce and study new extension of Rakočević's property $(w)$ and property $(b)$ introduced by Berkani--Zariouh in \cite{berkani-zariouh1}, in connection with other Weyl type theorems and recent properties. We prove in particular, the two following results: 1. A bounded linear operator $T$ satisfies property $(w_{π_{00}})$ if and only if $T$ satisfies property $(w)$ and $σ_{uf}(T)=σ_{uw}(T).$ 2. $T$ satisfies property $(gw_{π_{00}})$ if and only if $T$ satisfies property $(w_{π_{00}})$ and $π_{0}(T)=p_{0}^a(T).$ Classes of operators are considered as illustrating examples.
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