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Shine Lal Enose,Ramya Perumal,Prasad Thankarajan 대한수학회 2023 대한수학회논문집 Vol.38 No.4
In this paper, we study new classes of operators $k$-quasi $(\lowercase{m},\lowercase{n})$-paranormal operator, $k$-quasi $(\lowercase{m},\lowercase{n})^*$-paranormal operator, $k$-qu\-asi $(\lowercase{m},\lowercase{n})$-class~ $\mathcal{Q}$ operator and $k$-quasi $(\lowercase{m},\lowercase{n})$-class~ $\mathcal{Q^{*}}$ operator which are the generalization of $(\lowercase{m},\lowercase{n})$-paranormal and $(\lowercase{m},\lowercase{n})^*$-paranormal operators. We give matrix characterizations for $k$-quasi $(\lowercase{m},\lowercase{n})$-paranormal and $k$-quasi $(\lowercase{m},\lowercase{n})^*$-paranormal operators. Also we study some properties of $k$-quasi $(\lowercase{m},\lowercase{n})$-class~ $\mathcal{Q}$ operator and $k$-quasi $(\lowercase{m},\lowercase{n})$-class~ $\mathcal{Q}^*$ operators. Moreover, these classes of composition operators on $L^2$ spaces are characterized.