Recent zbMATH articles by "Rashid, Mohammad Hussein Mohammad"https://zbmath.org/atom/ai/rashid.mohammad-hussein-mohammad2024-03-13T18:33:02.981707ZWerkzeugSpectrum of \(k\)-quasi-class \(A_n\) operatorshttps://zbmath.org/1528.470022024-03-13T18:33:02.981707Z"Rashid, Mohammad H. M."https://zbmath.org/authors/?q=ai:rashid.mohammad-hussein-mohammadSummary: In this paper, we introduce a new class of operators, called \(k\)-quasi-class \(A_n\) operators, which is a superclass of class \(A\) and a subclass of \((n,k)\)-quasiparanormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that, if \(T\) is of \(k\)-quasi-class \(A_n\) then \(T-\lambda\) has finite ascent for all \(\lambda\in\mathbb{C}\). Also, we will prove \(T\) is polaroid and Weyl's theorem holds for \(T\) and \(f(T)\), where \(f\) is an analytic function in a neighborhood of the spectrum of \(T\). Moreover, we show that if \(\lambda\) is an isolated point of \(\sigma(T)\) and \(E\) is the Riesz idempotent of the spectrum of a \(k\)-quasi-class \(A_n\) operator \(T\), then \(E\mathscr{H} = \ker(T-\lambda)\) if \(\lambda\neq 0\) and \(E\mathscr{H} = \ker(T^{n+1})\) if \(\lambda = 0\).