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

Year 2018, Volume: 47 Issue: 6, 1564 - 1577, 12.12.2018

İlmi Hoxha Naim L. Braha Kotaro Tanahashi

Abstract

In this paper, we introduce a new class of operators, called $m$-quasi class $\mathcal{A}(k^{*})$ operators, which is a superclass of hyponormal operators and a subclass of absolute-$(k^{*},m)$-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 $\mathcal{A}(k^{*})$, then $\sigma _{np}(T)\setminus \{0\}=\sigma _{p}(T)\setminus \{0\}$, $\sigma _{na}(T)\setminus \{0\}=\sigma _{a}(T)\setminus \{0\}$ and $T-\mu $ has finite ascent for all $\mu\in\mathbb{C}.$ Also, we consider the tensor product of $m$-quasi class $\mathcal{A}(k^{*})$ operators.

Keywords

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

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