$n$-normal and $n$-quasinormal composition and weighted composition operators on $L^{2}(\mu)$

Authors

  • Anuradha Gupta Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi 110023, India Author
  • Neha Bhatia Department of Mathematics, University of Delhi, Delhi 110007, India Author

Keywords:

normal operator, quasinormal operator, $n$-normal operator, $n$-quasinormal operator, composition operator, weighted composition operator, conditional expectation operator, hyponormal operator, compact operator

Subjects:

47B20, 47B33, 47B38

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 compositionoperators and weighted composition operators become $n$-normaloperators and $n$-quasinormal operators have been obtained interms of Radon-Nikodym derivative $h_n$.

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Published

2014-10-15

Issue

Vol. 66 No. 4 (2014): Vol. 66, Issue 4

Section

Articles

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