局部化SVEP的伪半B-Fredholm和广义Drazin可逆算子
Pseudo semi B-Fredholm and Generalized Drazin invertible operators Through Localized SVEP
摘要：
本文定义并研究了巴拿赫空间中有界算子的伪上、下半B-Fredholm。特别地，我们证明了左广义Drazin谱与伪上半B-Fredholm谱在$S(T)$之前是相等的，$S(T )$是$T$不具有SVEP的集合.证明了左广义Drazin算子和右广义Drazin算子在可加交换幂有限秩扰动下的不变性，并给出了伪上下半B-弗雷德霍姆算子的一些扰动.作为应用，我们研究了超循环算子和乘子算子。进一步研究了上三角算子矩阵的左、右广义Drazin可逆性，给出了保证上三角算子矩阵的左、右广义Drazin谱或伪上、下半B-Fredholm是其对角项谱之并的充分条件。
英文摘要：
In this paper, we define and study the pseudo upper and lower semi B-Fredholm of bounded operators in a Banach space. In particular, we prove equality up to $S(T)$ between the left generalized Drazin spectrum and the pseudo upper semi B-Fredholm spectrum, $S(T )$ is the set where $T$ fails to have the SVEP. Also, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting power finite rank perturbations and some perturbations for the pseudo upper and lower semi B-Fredholm operators are given. As applications, we investigate some classes of operators as the supercyclic and multiplier operators. Furthermore, we investigate the left and the right generalized Drazin invertibility of upper triangular operator matrices by giving sufficient conditions which assure that the left and the right generalized Drazin spectrum or the pseudo upper and lower semi B-Fredholm of an upper triangular operator matrices is the union of its diagonal entries spectra.
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