On $m$-quasi class $\mathcal{A}(k^{*})$ and absolute-$(k^{*},m)$-paranormal operators

Authors : İlmi HOXHA, Naim L BRAHA, Kotaro TANAHASHİ

Pages : 1564-1577

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Publication Date : 2018-12-12

Article Type : Research Paper

Abstract :In this paper, we introduce a new class of operators, called $m$-quasi class $\mathcal{A}insert ignore into journalissuearticles values(k^{*});$ operators, which is a superclass of hyponormal operators and a subclass of absolute-$insert ignore into journalissuearticles values(k^{*},m);$-paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that if $T$ is $m$-quasi class $\mathcal{A}insert ignore into journalissuearticles values(k^{*});$, then $\sigma _{np}insert ignore into journalissuearticles values(T);\setminus \{0\}=\sigma _{p}insert ignore into journalissuearticles values(T);\setminus \{0\}$, $\sigma _{na}insert ignore into journalissuearticles values(T);\setminus \{0\}=\sigma _{a}insert ignore into journalissuearticles values(T);\setminus \{0\}$ and $T-\mu $ has finite ascent for all $\mu\in\mathbb{C}.$ Also, we consider the tensor product of $m$-quasi class $\mathcal{A}insert ignore into journalissuearticles values(k^{*});$ operators.
Keywords : m quasi class mathcal A k^, , absolute k^, m, paranormal