Generalized Kato decomposition, single-valued extension property and approximate point spectrum

作者：Jiang Qiaofen^*; Zhong Huaijie

来源：Journal of Mathematical Analysis and Applications, 2009, 356(1): 322-327.

DOI：10.1016/j.jmaa.2009.03.017

• Banach space
• Generalized Kato decomposition
• Single-valued extension property

In this paper, we define the generalized Kato spectrum of an operator, and obtain that the generalized Kato spectrum differs from the semi-regular spectrum on at most countably many points. We Study the localized version of the single-valued extension property at the points which are not limit points of the approximate point spectrum, as well as of the surjectivity spectrum. In particular, we shall characterize the single-valued extension property at a point lambda(0) is an element of C in the case that lambda(0)I - T admits a generalized Kato decomposition. From this characterization we shall deduce several results on cluster points of some distinguished parts of the spectrum.

• 出版日期2009-8-1
• 单位福建师范大学