Spectral Properties of <Emphasis Type="Italic">k</Emphasis>-Quasi-<Emphasis Type="Italic">M</Emphasis>-hyponormal Operators |
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Authors: | Fei Zuo Salah Mecheri |
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Institution: | 1.College of Mathematics and Information Science,Henan Normal University,Xinxiang,People’s Republic of China;2.College of Science Department of Mathematics,Taibah University,Al Madinah Al Munawarah,Saudi Arabia |
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Abstract: | In this paper, we study the k-quasi-M-hyponormal operator and mainly prove that if T is a k-quasi-M-hyponormal operator, then \(\sigma _{ja}(T)\backslash \{0\}=\sigma _{a}(T)\backslash \{0\}\), and the spectrum is continuous on the class of all k-quasi-M-hyponormal operators; let \(d_{AB}\in B(B(H))\) denote either the generalized derivation \(\delta _{AB}= L_{A}-R_{B}\) or the elementary operator \(\Delta _{AB} =L_{A}R_{B}- I\), we show that if A and \(B^{*}\) are k-quasi-M-hyponormal operators, then \(d_{AB}\) is polaroid and generalized Weyl’s theorem holds for \(f(d_{AB})\), where f is an analytic function on \(\sigma (d_{AB})\) and f is not constant on each connected component of the open set U containing \(\sigma (d_{AB})\). In additon, we discuss the hyperinvariant subspace problem for k-quasi-M-hyponormal operators. |
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