| $n$-normal and $n$-quasinormal composition and weighted composition operators on $L^{2}(\mu)$ |
| Anuradha Gupta and Neha Bhatia |
Abstract An operator $T$ is called $n$-normal operator if $T^nT^* = T^*T^n$ and $n$-quasinormal operator if $T^nT^*T = T^*TT^n$. In this paper, the conditions under which composition operators and weighted composition operators become $n$-normal operators and $n$-quasinormal operators have been obtained in terms of Radon-Nikodym derivative $h_n$.
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Keywords: normal operator; quasinormal operator; $n$-normal operator; $n$-quasinormal operator; composition operator; weighted composition operator; conditional expectation operator; hyponormal operator; compact operator. |
MSC: 47B20, 47B33, 47B38 |
Pages: 364$-$370 |
Volume 66 , Issue 4 , 2014 |
