New approach to a-Weyl’s theorem and some preservation results
New approach to a-Weyl’s theorem and some preservation results
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a-Weyl 定理的新方法和一些保留结果
DOI：
10.1007/s12215-020-00525-2
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
H. Zariouh
中科院分区：
文献类型：
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作者：
K. Ben Ouidren;H. Zariouh
本文引入并研究了与a-Weyl型定理有关的新的谱性质（bz）和（bz），它们分别类似于a-Weyl定理和a-Browder定理。其中，我们证明了有界线性算子T满足性质（bz）当且仅当T满足Browder定理，其中和分别是上半Fredholm谱和上Weyl谱.此外，通过局部SVEP刻画了算子T的性质（bz），并讨论了它在两个有界线性算子直和下的保持性.该理论的例子中的一些特殊类别的运营商。我们还证明了下面的新结果， σ UF ( 不 ) = σ uw ( 不 ) ⟺ σ UBF ( 不 ) = σ UBW ( 不 ) , 对每个有界线性算子T.
In this paper, we introduce and study new spectral properties called (bz) andin connection with a-Weyl type theorems, which are analogous respectively to a-Weyl’s theorem and a-Browder’s theorem. Among other results, we prove that a bounded linear operatorTsatisfies property (bz) if and only ifTsatisfies a-Browder’s theorem andwhereandare respectively, the upper semi-Fredholm spectrum and the upper Weyl spectrum. Furthermore, the property (bz) is characterized for an operatorTthrough localized SVEP, and its preservation under direct sum of two bounded linear operators is also examined. The theory is exemplified in the case of some special classes of operators. We also prove the following new result that’s σ uf ( T ) = σ uw ( T ) ⟺ σ ubf ( T ) = σ ubw ( T ) , for every bounded linear operatorT.