A Characterization of Some Subsets of Essential Spectra of a Multivalued Linear Operator

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• 作者：Aymen Ammar
• 关键词：Atkinson linear relations ; Essential spectra ; Left (resp. right)generalized inverse multivalued operator
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：11
• 期：1
• 页码：175-196
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Operator Theory; Analysis;
• 出版者：Springer International Publishing
• ISSN：1661-8262
• 卷排序：11

文摘

In the present paper, we characterize some essential spectra of a closed linear relation in terms of certain linear relations type \(\mathbf{ \alpha }\)-and \(\beta \)-Atkinson. This study leads us to generalize some well-known results for operators and to extend some results of small perturbations given by Álvarez and Wilcox in [6]. In the same way, we present the perturbation classes of \(\alpha \)- and \(\beta \)- Atkinson linear relations (see Theorem 3.3).