Characterization of closed n-paranormal and \(n^{*}\)-paranormal operators

IF 0.5 Q3 MATHEMATICS
Salah Mecheri, Aissa Nasli Bakir
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引用次数: 0

Abstract

We give several basic and spectral properties of classes of closed n-paranormal and closed \(n^{*}\)-paranormal operators on dense domains in complex separable Hilbert spaces. We prove that for both of these classes of operators, the null space of \((T-\mu I)\) and the range of \(R(E_{\mu })\) are identical, where \(E_{\mu }\) is the Riesz projection with respect to an isolated point \(\mu \) of the spectrum. We show that they satisfy Weyl’s theorem. Certain properties related to the reduced minimum modulus are also established.

封闭 n-paranormal 和 $$n^{*}$$ n ∗ -paranormal 算子的特征
我们给出了复可分希尔伯特空间中密集域上的闭 n-paranormal 和闭\(n^{*}\)-paranormal 算子类的几个基本性质和谱性质。我们证明,对于这两类算子,\((T-\mu I)\)的空域和\(R(E_{\mu })\)的范围是相同的,其中\(E_{\mu }\)是关于谱的孤立点\(\mu \)的里兹投影。我们证明它们满足韦尔定理。我们还建立了与减小的最小模量相关的某些性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
39
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