Weyl Type Theorems for Left and Right Polaroid Operators
Weyl Type Theorems for Left and Right Polaroid Operators
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DOI：
10.1007/s00020-009-1738-2
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发表时间：
2010-01
影响因子：
0.8
通讯作者：
P. Aiena;Elvis Aponte;Edixon Balzan
中科院分区：
文献类型：
--
作者：
P. Aiena;Elvis Aponte;Edixon Balzan
在巴拿赫空间上定义的有界算子，如果谱上的每个孤立点都是解旋的极点，则称为偏光算子。本文考虑了左偏立得和右偏立得两个相关概念，并结合偏立得的条件进行了探讨。此外，还研究了左、右偏光算子的Weyl型定理和广义Weyl型定理的等价性。因此，我们获得了一个通用的框架，它允许我们以统一的方式导出许多关于Weyl类型定理（广义或非广义）的重要操作符类的最新结果。
A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of beinga-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.