@article{ba3bec15761148a198eb5734e6ab034b,
title = "On local spectral properties of operator matrices",
abstract = "In this paper, we focus on a 2 × 2 operator matrix Tϵk as follows: Tϵk=(ACϵkDB), where ϵk is a positive sequence such that lim k→∞ϵk= 0. We first explore how Tϵk has several local spectral properties such as the single-valued extension property, the property (β) , and decomposable. We next study the relationship between some spectra of Tϵk and spectra of its diagonal entries, and find some hypotheses by which Tϵk satisfies Weyl{\textquoteright}s theorem and a-Weyl{\textquoteright}s theorem. Finally, we give some conditions that such an operator matrix Tϵk has a nontrivial hyperinvariant subspace.",
keywords = "2 × 2 operator matrices, Decomposable, Hyperinvariant subspace, The property (β), The single-valued extension property, Weyl{\textquoteright}s theorem",
author = "An, {Il Ju} and Eungil Ko and Lee, {Ji Eun}",
note = "Funding Information: Il Ju An was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01006036). Eungil Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058633) and the Ministry of Education (2019R1A6A1A11051177). Ji Eun Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1A2C1002653). Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
doi = "10.1186/s13660-021-02697-6",
language = "English",
volume = "2021",
journal = "Journal of Inequalities and Applications",
issn = "1025-5834",
publisher = "Springer Open",
number = "1",
}