Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-10-22 , DOI: 10.1080/03081087.2020.1833823 Kaoutar Ben Ouidren 1 , Hassan Zariouh 2
ABSTRACT
In this paper, we study the properties and which we had introduced in [Ben Ouidren K, Zariouh H. New approach to a-Weyl's theorem and some preservation results. Rend Circ Mat Palermo. doi: 10.1007/s12215-020-00525-2], for an operator having the SVEP on the complementary of distinguished parts of its spectrum. We prove in particular, that a bounded linear operator T acting on a Banach space has the SVEP on the complementary of if and only if T possesses property We also study the stability of these properties under several commuting perturbations, and we prove that if T possesses property then possesses property for every Riesz operator R commuting with T and We also give an example which shows that the property is generally unstable under this type of perturbations, and we prove that if T possesses property then T + R possesses property ⇔ Analogous results are proved for the property and some applications to the class of a-isoloid-type operators are given.
中文翻译:
通过局部 SVEP 和 Riesz 型扰动实现 a-Weyl 定理的新方法
摘要
在本文中,我们研究了属性和我们在 [Ben Ouidren K, Zariouh H. 中介绍了 a-Weyl 定理的新方法和一些保存结果。撕裂 Circ Mat 巴勒莫。doi: 10.1007/s12215-020-00525-2],适用于在其频谱的显着部分互补上具有 SVEP 的运营商。我们特别证明了作用于 Banach 空间的有界线性算子T的 SVEP 在当且仅当T拥有财产我们还研究了这些性质在几种通勤扰动下的稳定性,并证明了如果T具有性质然后拥有财产对于每个 Riesz 算子R与T和我们还举了一个例子来说明属性在这种类型的扰动下通常是不稳定的,我们证明如果T具有性质那么T + R拥有属性⇔类似的结果也证明了性质并给出了a-isoroid-type算子类的一些应用。