We introduce a new class which generalizes the class of B-Weyl operators. Wesay that $T\in L(X)$ is pseudo B-Weyl if $T=T_1\oplus T_2$ where $T_1$ is aWeyl operator and $T_2$ is a quasi-nilpotent operator. We show that thecorresponding pseudo B-Weyl spectrum $\sigma_{pBW}(T)$ satisfies the equality$\sigma_{pBW}(T)\cup[{\mathcal S}(T)\cap{\mathcal S}(T^*)]=\sigma_{gD}(T);$where $\sigma_{gD}(T)$ is the generalized Drazin spectrum of $T\in L(X)$ and${\mathcal S}(T)$ (resp., ${\mathcal S} (T^*)$) is the set where $T$ (resp.,$T^*$) fails to have SVEP. We also investigate the generalized Drazininvertibility of upper triangular operator matrices by giving sufficientconditions which assure that the generalized Drazin spectrum or the pseudoB-Weyl spectrum of an upper triangular operator matrices is the union of itsdiagonal entries spectra.
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机译：我们引入了一个新的类，它推广了B-Weyl算子的类。如果$ T = T_1 \ oplus T_2 $，其中$ T_1 $是Weyl算子，而$ T_2 $是准幂等算子，则我们假设L（X）$中的$ T \是伪B-Weyl。我们证明了对应的伪B-魏尔谱$ \ sigma_ {pBW}（T）$满足等式$ \ sigma_ {pBW}（T）\ cup [{\ mathcal S}（T）\ cap {\ mathcal S}（ T ^ *）] = \ sigma_ {gD}（T）; $，其中$ \ sigma_ {gD}（T）$是L（X）$和$ {\ mathcal S}（ T）$（分别是$ {\ mathcal S}（T ^ *）$）是其中$ T $（分别是$ T ^ * $）没有SVEP的集合。我们还通过给出足够的条件来研究上三角算子矩阵的广义Drazin可逆性，以确保上三角算子矩阵的广义Drazin谱或拟B-Weyl谱是其对角项谱的并集。
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